In [1]:
from sympy import *; init_session()
IPython console for SymPy 0.7.6 (Python 2.7.9-64-bit) (ground types: python)
These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)
>>> init_printing()
Documentation can be found at http://www.sympy.org
In [2]:
%matplotlib inline
In [3]:
from applpy import *
In [4]:
X = ExponentialRV(Rational(1,100))
In [5]:
X.display()
continuous pdf
for 0 <= x <= oo
---------------------------
-x
───
100
ℯ
────
100
---------------------------
In [6]:
CDF(X)
continuous cdf
for 0 <= x <= oo
---------------------------
-x
───
100
1 - ℯ
---------------------------
Out[6]:
None
In [7]:
HF(X)
continuous hf
for 0 <= x <= oo
---------------------------
1/100
---------------------------
Out[7]:
None
In [8]:
XX = ExponentialRV()
In [9]:
XX.display()
continuous pdf
for 0 <= x <= oo
---------------------------
-θ⋅x
θ⋅ℯ
---------------------------
In [10]:
CDF(XX)
continuous cdf
for 0 <= x <= oo
---------------------------
-θ⋅x
1 - ℯ
---------------------------
Out[10]:
None
In [11]:
Inv1 = TriangularRV(-2,1,3)
In [12]:
Inv2 = TriangularRV(-10,3,20)
In [13]:
Inv3 = TriangularRV(-4, 3, 5)
In [14]:
PlotDist(Inv1)
In [15]:
Portfolio = Inv1 + Inv2
In [16]:
Portfolio.display()
continuous pdf
for -12 <= x <= -10
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 4⋅log ⎝ℯ ⎠ 16⋅log⎝ℯ ⎠ 64
──────── + ────────── + ────────── + ───
8775 975 325 325
---------------------------
for -10 <= x <= -9
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 4⋅log ⎝ℯ ⎠ 16⋅log⎝ℯ ⎠ 64
──────── + ────────── + ────────── + ───
8775 975 325 325
---------------------------
for -9 <= x <= -7
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 7⋅log ⎝ℯ ⎠ log⎝ℯ ⎠ 7
- ──────── - ────────── - ─────── - ───
5850 1950 50 650
---------------------------
for -7 <= x <= -2
---------------------------
⎛ x⎞
log⎝ℯ ⎠ 28
─────── + ───
195 585
---------------------------
for -2 <= x <= 0
---------------------------
⎛ x⎞
log⎝ℯ ⎠ 28
─────── + ───
195 585
---------------------------
for 0 <= x <= 1
---------------------------
⎛ x⎞
log⎝ℯ ⎠ 28
─────── + ───
195 585
---------------------------
for 1 <= x <= 3
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ log⎝ℯ ⎠ 478
- ────────── + ────────── + ─────── + ────
9945 3315 221 9945
---------------------------
for 3 <= x <= 4
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ log⎝ℯ ⎠ 478
- ────────── + ────────── + ─────── + ────
9945 3315 221 9945
---------------------------
for 4 <= x <= 6
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 6⋅log ⎝ℯ ⎠ 19⋅log⎝ℯ ⎠ 158
──────── - ────────── + ────────── + ────
3315 1105 663 9945
---------------------------
for 6 <= x <= 18
---------------------------
⎛ x⎞
log⎝ℯ ⎠ 62
- ─────── + ───
255 765
---------------------------
for 18 <= x <= 20
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 103⋅log⎝ℯ ⎠ 1634
──────── - ────────── + ─────────── - ────
11475 425 1275 3825
---------------------------
for 20 <= x <= 21
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 103⋅log⎝ℯ ⎠ 1634
──────── - ────────── + ─────────── - ────
11475 425 1275 3825
---------------------------
for 21 <= x <= 23
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 23⋅log ⎝ℯ ⎠ 529⋅log⎝ℯ ⎠ 12167
- ──────── + ─────────── - ─────────── + ─────
7650 2550 2550 7650
---------------------------
In [17]:
PlotDist(Portfolio)
In [18]:
Mean(Portfolio).evalf()
Out[18]:
$$5.0$$
In [19]:
CDF(Portfolio,0).evalf()
Out[19]:
$$0.226068376068376$$
In [20]:
Portfolio2 = Portfolio + Inv3
In [22]:
Portfolio2.display()
continuous pdf
for -16 <= x <= -14
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 8⋅log ⎝ℯ ⎠ 256⋅log ⎝ℯ ⎠ 4096⋅log ⎝ℯ ⎠ 32768⋅log⎝ℯ ⎠ 524288
──────── + ────────── + ──────────── + ───────────── + ───────────── + ───────
5528250 552825 552825 552825 552825 2764125
---------------------------
for -14 <= x <= -13
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 8⋅log ⎝ℯ ⎠ 256⋅log ⎝ℯ ⎠ 4096⋅log ⎝ℯ ⎠ 32768⋅log⎝ℯ ⎠ 524288
──────── + ────────── + ──────────── + ───────────── + ───────────── + ───────
5528250 552825 552825 552825 552825 2764125
---------------------------
for -13 <= x <= -12
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 11⋅log ⎝ℯ ⎠ 37⋅log ⎝ℯ ⎠ 133⋅log ⎝ℯ ⎠ 3911⋅log⎝ℯ ⎠ 26743
- ──────── - ─────────── - ─────────── - ──────────── - ──────────── + ───────
3685500 737100 122850 52650 737100 1228500
---------------------------
for -12 <= x <= -11
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 11⋅log ⎝ℯ ⎠ 37⋅log ⎝ℯ ⎠ 133⋅log ⎝ℯ ⎠ 3911⋅log⎝ℯ ⎠ 26743
- ──────── - ─────────── - ─────────── - ──────────── - ──────────── + ───────
3685500 737100 122850 52650 737100 1228500
---------------------------
for -11 <= x <= -10
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 8⋅log ⎝ℯ ⎠ 1073⋅log⎝ℯ ⎠ 928
──────── + ────────── + ──────────── + ─────
36855 7371 73710 14175
---------------------------
for -10 <= x <= -9
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 8⋅log ⎝ℯ ⎠ 1073⋅log⎝ℯ ⎠ 928
──────── + ────────── + ──────────── + ─────
36855 7371 73710 14175
---------------------------
for -9 <= x <= -7
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 233⋅log ⎝ℯ ⎠ 1787⋅log ⎝ℯ ⎠ 1279⋅log⎝ℯ ⎠ 64133
- ──────── - ──────── - ──────────── - ───────────── - ──────────── + ───────
1228500 27300 368550 368550 105300 3685500
---------------------------
for -7 <= x <= -6
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 8⋅log ⎝ℯ ⎠ 178⋅log ⎝ℯ ⎠ 296⋅log ⎝ℯ ⎠ 359⋅log⎝ℯ ⎠ 77512
- ──────── - ────────── - ──────────── - ──────────── - ─────────── + ───────
5528250 552825 552825 110565 78975 2764125
---------------------------
for -6 <= x <= -5
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 103⋅log ⎝ℯ ⎠ 227⋅log ⎝ℯ ⎠ 38⋅log ⎝ℯ ⎠ 4777⋅log⎝ℯ ⎠ 1212
─────────── + ──────────── + ──────────── + ─────────── + ──────────── + ─────
22113000 2211300 552825 22113 552825 27641
52
──
25
---------------------------
for -5 <= x <= -4
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 103⋅log ⎝ℯ ⎠ 227⋅log ⎝ℯ ⎠ 38⋅log ⎝ℯ ⎠ 4777⋅log⎝ℯ ⎠ 1212
─────────── + ──────────── + ──────────── + ─────────── + ──────────── + ─────
22113000 2211300 552825 22113 552825 27641
52
──
25
---------------------------
for -4 <= x <= -3
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 133⋅log⎝ℯ ⎠ 5396
- ──────── - ──────── - ──────── - ────────── + ─────────── + ──────
1053000 105300 26325 26325 26325 131625
---------------------------
for -3 <= x <= -2
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
53⋅log ⎝ℯ ⎠ 179⋅log ⎝ℯ ⎠ 209⋅log ⎝ℯ ⎠ 508⋅log ⎝ℯ ⎠ 15422⋅log⎝ℯ ⎠
- ─────────── - ──────────── - ──────────── - ──────────── + ───────────── + ─
41769000 12530700 3132675 3132675 3132675 1
640909
───────
5663375
---------------------------
for -2 <= x <= -1
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 116⋅log⎝ℯ ⎠ 4751
- ──────── - ──────── - ────────── - ────────── + ─────────── + ──────
3132675 208845 69615 23205 23205 116025
---------------------------
for -1 <= x <= 0
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 116⋅log⎝ℯ ⎠ 4751
- ──────── - ──────── - ────────── - ────────── + ─────────── + ──────
3132675 208845 69615 23205 23205 116025
---------------------------
for 0 <= x <= 1
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 116⋅log⎝ℯ ⎠ 4751
──────── - ──────── - ────────── - ────────── + ─────────── + ──────
2088450 208845 69615 23205 23205 116025
---------------------------
for 1 <= x <= 2
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 116⋅log⎝ℯ ⎠ 4751
──────── - ──────── - ────────── - ────────── + ─────────── + ──────
2088450 208845 69615 23205 23205 116025
---------------------------
for 2 <= x <= 3
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 148⋅log⎝ℯ ⎠ 1711
- ────────── - ────────── + ─────────── + ─────
41769 41769 29835 41769
---------------------------
for 3 <= x <= 4
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
2⋅log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 148⋅log⎝ℯ ⎠ 1711
- ────────── - ────────── + ─────────── + ─────
41769 41769 29835 41769
---------------------------
for 4 <= x <= 5
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 38⋅log ⎝ℯ ⎠ 202⋅log ⎝ℯ ⎠ 284⋅log⎝ℯ ⎠ 41239
──────── - ────────── + ─────────── - ──────────── + ─────────── + ───────
696150 69615 208845 208845 41769 1044225
---------------------------
for 5 <= x <= 6
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 2⋅log ⎝ℯ ⎠ 38⋅log ⎝ℯ ⎠ 202⋅log ⎝ℯ ⎠ 284⋅log⎝ℯ ⎠ 41239
──────── - ────────── + ─────────── - ──────────── + ─────────── + ───────
696150 69615 208845 208845 41769 1044225
---------------------------
for 6 <= x <= 7
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 46⋅log ⎝ℯ ⎠ 302⋅log ⎝ℯ ⎠ 92⋅log⎝ℯ ⎠ 50311
──────── + ──────── - ─────────── + ──────────── - ────────── + ───────
3132675 208845 208845 208845 208845 1044225
---------------------------
for 7 <= x <= 8
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 109⋅log ⎝ℯ ⎠ 827⋅log ⎝ℯ ⎠ 5749⋅log ⎝ℯ ⎠ 36383⋅log⎝ℯ ⎠
- ─────────── + ──────────── - ──────────── + ───────────── - ───────────── +
12530700 835380 417690 417690 835380
34873
──────
321300
---------------------------
for 8 <= x <= 9
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 109⋅log ⎝ℯ ⎠ 827⋅log ⎝ℯ ⎠ 5749⋅log ⎝ℯ ⎠ 36383⋅log⎝ℯ ⎠
- ─────────── + ──────────── - ──────────── + ───────────── - ───────────── +
12530700 835380 417690 417690 835380
34873
──────
321300
---------------------------
for 9 <= x <= 11
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 11⋅log ⎝ℯ ⎠ 121⋅log ⎝ℯ ⎠ 1331⋅log ⎝ℯ ⎠ 14173⋅log⎝ℯ ⎠ 109571
──────── - ─────────── + ──────────── - ───────────── + ───────────── - ──────
596700 119340 59670 59670 119340 596700
---------------------------
for 11 <= x <= 14
---------------------------
⎛ x⎞
log⎝ℯ ⎠ 22
- ─────── + ───
255 255
---------------------------
for 14 <= x <= 16
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 28⋅log ⎝ℯ ⎠ 392⋅log ⎝ℯ ⎠ 2339⋅log⎝ℯ ⎠ 6134
──────── - ──────── + ─────────── - ──────────── + ──────────── + ──────
7229250 103275 103275 103275 103275 516375
---------------------------
for 16 <= x <= 17
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 28⋅log ⎝ℯ ⎠ 392⋅log ⎝ℯ ⎠ 2339⋅log⎝ℯ ⎠ 6134
──────── - ──────── + ─────────── - ──────────── + ──────────── + ──────
7229250 103275 103275 103275 103275 516375
---------------------------
for 17 <= x <= 18
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 19⋅log ⎝ℯ ⎠ 13⋅log ⎝ℯ ⎠ 6359⋅log ⎝ℯ ⎠ 117371⋅log⎝ℯ ⎠ 807
- ──────── + ─────────── - ─────────── + ───────────── - ────────────── + ────
4819500 963900 17850 481950 963900 1606
893
───
500
---------------------------
for 18 <= x <= 19
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 19⋅log ⎝ℯ ⎠ 13⋅log ⎝ℯ ⎠ 6359⋅log ⎝ℯ ⎠ 117371⋅log⎝ℯ ⎠ 807
- ──────── + ─────────── - ─────────── + ───────────── - ────────────── + ────
4819500 963900 17850 481950 963900 1606
893
───
500
---------------------------
for 19 <= x <= 20
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 10⋅log ⎝ℯ ⎠ 37⋅log⎝ℯ ⎠ 2621
──────── - ─────────── + ────────── - ──────
48195 9639 2754 240975
---------------------------
for 20 <= x <= 21
---------------------------
3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 10⋅log ⎝ℯ ⎠ 37⋅log⎝ℯ ⎠ 2621
──────── - ─────────── + ────────── - ──────
48195 9639 2754 240975
---------------------------
for 21 <= x <= 23
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 1313⋅log ⎝ℯ ⎠ 27283⋅log ⎝ℯ ⎠ 81499⋅log⎝ℯ ⎠ 12199
- ──────── + ──────── - ───────────── + ────────────── - ───────────── + ─────
1606500 15300 481950 481950 137700 48195
883
───
00
---------------------------
for 23 <= x <= 24
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ log ⎝ℯ ⎠ 118⋅log ⎝ℯ ⎠ 332⋅log ⎝ℯ ⎠ 8836⋅log⎝ℯ ⎠ 2113688
- ──────── + ──────── - ──────────── - ──────────── + ──────────── - ───────
7229250 103275 722925 144585 103275 3614625
---------------------------
for 24 <= x <= 25
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 128⋅log ⎝ℯ ⎠ 6362⋅log ⎝ℯ ⎠ 31436⋅log ⎝ℯ ⎠ 1928092⋅log⎝ℯ ⎠
─────────── - ──────────── + ───────────── - ────────────── + ───────────────
28917000 722925 722925 144585 722925
46903448
- ────────
3614625
---------------------------
for 25 <= x <= 26
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
41⋅log ⎝ℯ ⎠ 128⋅log ⎝ℯ ⎠ 6362⋅log ⎝ℯ ⎠ 31436⋅log ⎝ℯ ⎠ 1928092⋅log⎝ℯ ⎠
─────────── - ──────────── + ───────────── - ────────────── + ───────────────
28917000 722925 722925 144585 722925
46903448
- ────────
3614625
---------------------------
for 26 <= x <= 28
---------------------------
5⎛ x⎞ 4⎛ x⎞ 3⎛ x⎞ 2⎛ x⎞ ⎛ x⎞
log ⎝ℯ ⎠ 7⋅log ⎝ℯ ⎠ 196⋅log ⎝ℯ ⎠ 5488⋅log ⎝ℯ ⎠ 76832⋅log⎝ℯ ⎠ 21512
- ──────── + ────────── - ──────────── + ───────────── - ───────────── + ─────
1377000 68850 34425 34425 34425 1721
96
──
25
---------------------------
In [23]:
PlotDist(Portfolio2)
In [24]:
CDF(Portfolio2, 0).evalf()
Out[24]:
$$0.176314491608609$$
In [25]:
Mean(Portfolio2).evalf()
Out[25]:
$$6.33333333333333$$
In [26]:
[Variance(Portfolio).evalf() , Variance(Portfolio2).evalf()]
Out[26]:
$$\left [ 38.7777777777778, \quad 42.5\right ]$$
In [27]:
Mean(X)
Out[27]:
$$100$$
In [28]:
X2 = Maximum(X,X)
In [29]:
X2.display()
continuous pdf
for 0 <= x <= oo
---------------------------
2
⎛ x ⎞ -x ⎛ x ⎞ -x
⎜ ─── ⎟ ─── ⎜ ─── ⎟ ───
⎜ 100 ⎟ 50 ⎜ 100 ⎟ 100
⎝ℯ - 1⎠ ⋅ℯ ⎝ℯ - 1⎠⋅ℯ
- ──────────────── + ───────────────
50 50
---------------------------
In [30]:
Mean(X2)
Out[30]:
$$150$$
In [31]:
for i in range(1,11):
print i
Sys2 = MaximumIID(X,i)
Sys2.display()
print Mean(Sys2).evalf()
print Sys2.variate(s=0.1)
1
continuous pdf
for 0 <= x <= oo
---------------------------
-x
───
100
ℯ
────
100
---------------------------
100.000000000000
[10.5360515657826]
2
continuous pdf
for 0 <= x <= oo
---------------------------
2
⎛ x ⎞ -x ⎛ x ⎞ -x
⎜ ─── ⎟ ─── ⎜ ─── ⎟ ───
⎜ 100 ⎟ 50 ⎜ 100 ⎟ 100
⎝ℯ - 1⎠ ⋅ℯ ⎝ℯ - 1⎠⋅ℯ
- ──────────────── + ───────────────
50 50
---------------------------
150.000000000000
[38.0130408066172]
3
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -3⋅x
─── ─── ─────
50 100 100
3⋅ℯ 3⋅ℯ 3⋅ℯ
- ────── + ────── + ────────
50 100 100
---------------------------
183.333333333333
[62.3917586035155]
4
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -x -3⋅x
─── ─── ─── ─────
25 50 100 100
ℯ 3⋅ℯ ℯ 3⋅ℯ
- ──── - ────── + ──── + ────────
25 25 25 25
---------------------------
208.333333333333
[82.6315953659673]
5
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -x -x -3⋅x
─── ─── ─── ─── ─────
20 25 50 100 100
ℯ ℯ ℯ ℯ 3⋅ℯ
──── - ──── - ──── + ──── + ────────
20 5 5 20 10
---------------------------
228.333333333333
[99.6843044007847]
6
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -x -3⋅x -x -3⋅x
─── ─── ─── ───── ─── ─────
20 25 50 50 100 100
3⋅ℯ 3⋅ℯ 3⋅ℯ 3⋅ℯ 3⋅ℯ 3⋅ℯ
────── - ────── - ────── - ──────── + ────── + ────────
10 5 10 50 50 5
---------------------------
245.000000000000
[114.348017257812]
7
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -x -3⋅x -x -3⋅x -7⋅x
─── ─── ─── ───── ─── ───── ─────
20 25 50 50 100 100 100
21⋅ℯ 7⋅ℯ 21⋅ℯ 21⋅ℯ 7⋅ℯ 21⋅ℯ 7⋅ℯ
─────── - ────── - ─────── - ───────── + ────── + ───────── + ────────
20 5 50 50 100 20 100
---------------------------
259.285714285714
[127.184370902862]
8
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -2⋅x -x -3⋅x -x -3⋅x
─── ─── ───── ─── ───── ─── ─────
20 25 25 50 50 100 100
14⋅ℯ 14⋅ℯ 2⋅ℯ 14⋅ℯ 42⋅ℯ 2⋅ℯ 42⋅ℯ 14⋅ℯ
─────── - ─────── - ──────── - ─────── - ───────── + ────── + ───────── + ────
5 5 25 25 25 25 25
-7⋅x
─────
100
─────
25
---------------------------
271.785714285714
[138.587128795779]
9
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -2⋅x -x -3⋅x -x -3⋅x
─── ─── ───── ─── ───── ─── ─────
20 25 25 50 50 100 100
63⋅ℯ 126⋅ℯ 18⋅ℯ 18⋅ℯ 126⋅ℯ 9⋅ℯ 63⋅ℯ 6
─────── - ──────── - ───────── - ─────── - ────────── + ────── + ───────── + ─
10 25 25 25 25 100 25
-7⋅x -9⋅x
───── ─────
100 100
3⋅ℯ 9⋅ℯ
──────── + ────────
25 100
---------------------------
282.896825396825
[148.838769840507]
10
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -x -2⋅x -x -3⋅x -x -3⋅x
─── ─── ─── ───── ─── ───── ─── ─────
10 20 25 25 50 50 100 100
ℯ 63⋅ℯ 42⋅ℯ 18⋅ℯ 9⋅ℯ 63⋅ℯ ℯ 18⋅ℯ
- ──── + ─────── - ─────── - ───────── - ────── - ───────── + ──── + ─────────
10 5 5 5 10 5 10 5
-7⋅x -9⋅x
───── ─────
100 100
42⋅ℯ 9⋅ℯ
+ ───────── + ────────
5 10
---------------------------
292.896825396825
[158.147375340846]
In [32]:
System2 = Minimum(X, Minimum(Maximum(X,X) , Maximum(X,X)))
In [33]:
System2.display()
continuous pdf
for 0 <= x <= oo
---------------------------
-x -x -3⋅x
─── ─── ─────
20 25 100
ℯ 4⋅ℯ 3⋅ℯ
──── - ────── + ────────
20 25 25
---------------------------
In [34]:
BallBearing = [17.88, 28.92, 33.00, 41.52, 42.12, 45.60, 48.48, 51.84, 51.96, 54.12, 55.56, 67.80, 68.64,
68.64, 68.88, 84.12, 93.12, 98.64, 105.12, 105.84, 127.92, 128.04, 173.40]
In [35]:
len(BallBearing)
Out[35]:
$$23$$
In [36]:
Bstar = BootstrapRV(BallBearing)
In [37]:
Bstar.display()
discrete pdf where {x->f(x)}:
{17.88 -> 1/23}, {28.92 -> 1/23}, {33.0 -> 1/23}, {41.52 -> 1/23}, {42.12 -> 1/23}, {45.6 -> 1/23}, {48.48 -> 1/23}, {51.84 -> 1/23}, {51.96 -> 1/23}, {54.12 -> 1/23}, {55.56 -> 1/23}, {67.8 -> 1/23}, {68.64 -> 2/23}, {68.88 -> 1/23}, {84.12 -> 1/23}, {93.12 -> 1/23}, {98.64 -> 1/23}, {105.12 -> 1/23}, {105.84 -> 1/23}, {127.92 -> 1/23}, {128.04 -> 1/23}, {173.4 -> 1/23}
In [38]:
PlotDist(CDF(Bstar))
In [39]:
Sys2 = MaximumIID(Bstar,2)
In [40]:
Sys2.display()
discrete pdf where {x->f(x)}:
{17.88 -> 1/529}, {28.92 -> 3/529}, {33.0 -> 5/529}, {41.52 -> 7/529}, {42.12 -> 9/529}, {45.6 -> 11/529}, {48.48 -> 13/529}, {51.84 -> 15/529}, {51.96 -> 17/529}, {54.12 -> 19/529}, {55.56 -> 21/529}, {67.8 -> 1/23}, {68.64 -> 52/529}, {68.88 -> 29/529}, {84.12 -> 31/529}, {93.12 -> 33/529}, {98.64 -> 35/529}, {105.12 -> 37/529}, {105.84 -> 39/529}, {127.92 -> 41/529}, {128.04 -> 43/529}, {173.4 -> 45/529}
In [41]:
PlotDist(PDF(Sys2))
In [42]:
PlotDist(CDF(Sys2))
In [43]:
[Mean(Bstar), Mean(Sys2)]
Out[43]:
$$\left [ 72.224347826087, \quad 92.168393194707\right ]$$
In [44]:
Sys3 = ConvolutionIID(Bstar,3)
In [45]:
Sys3.display()
discrete pdf where {x->f(x)}:
{53.64 -> 1/12167}, {64.68 -> 2/12167}, {64.68 -> 1/12167}, {68.76 -> 3/12167}, {75.72 -> 3/12167}, {77.28 -> 3/12167}, {77.88 -> 3/12167}, {79.8 -> 6/12167}, {81.36 -> 3/12167}, {83.88 -> 3/12167}, {84.24 -> 3/12167}, {86.76 -> 1/12167}, {87.6 -> 3/12167}, {87.72 -> 3/12167}, {88.32 -> 4/12167}, {88.32 -> 2/12167}, {88.92 -> 4/12167}, {88.92 -> 2/12167}, {89.88 -> 3/12167}, {90.84 -> 3/12167}, {91.32 -> 3/12167}, {92.4 -> 12/12167}, {93.0 -> 6/12167}, {94.92 -> 3/12167}, {95.28 -> 6/12167}, {96.48 -> 4/12167}, {96.48 -> 2/12167}, {98.64 -> 6/12167}, {98.76 -> 4/12167}, {98.76 -> 2/12167}, {99.0 -> 1/12167}, {99.36 -> 4/12167}, {99.36 -> 4/12167}, {99.36 -> 1/12167}, {99.96 -> 2/12167}, {99.96 -> 1/12167}, {100.92 -> 4/12167}, {100.92 -> 3/12167}, {100.92 -> 2/12167}, {101.52 -> 2/12167}, {101.52 -> 4/12167}, {102.12 -> 1/12167}, {102.12 -> 2/12167}, {102.36 -> 6/12167}, {102.72 -> 6/12167}, {102.84 -> 6/12167}, {103.44 -> 5/12167}, {103.44 -> 4/12167}, {103.56 -> 2/12167}, {103.56 -> 1/12167}, {104.04 -> 4/12167}, {104.04 -> 2/12167}, {104.4 -> 4/12167}, {104.4 -> 2/12167}, {104.64 -> 3/12167}, {105.0 -> 12/12167}, {105.6 -> 6/12167}, {106.32 -> 1/12167}, {106.32 -> 2/12167}, {106.44 -> 6/12167}, {107.52 -> 2/12167}, {107.52 -> 7/12167}, {107.88 -> 6/12167}, {108.12 -> 3/12167}, {108.48 -> 6/12167}, {109.08 -> 1/12167}, {109.08 -> 2/12167}, {109.68 -> 3/12167}, {109.8 -> 2/12167}, {109.8 -> 1/12167}, {110.4 -> 2/12167}, {110.4 -> 4/12167}, {111.24 -> 6/12167}, {111.36 -> 2/12167}, {111.36 -> 4/12167}, {111.6 -> 3/12167}, {111.84 -> 6/12167}, {111.96 -> 6/12167}, {111.96 -> 12/12167}, {112.56 -> 6/12167}, {113.16 -> 3/12167}, {113.4 -> 3/12167}, {113.52 -> 2/12167}, {113.52 -> 4/12167}, {113.76 -> 6/12167}, {113.88 -> 4/12167}, {113.88 -> 2/12167}, {114.12 -> 2/12167}, {114.12 -> 4/12167}, {114.48 -> 3/12167}, {114.6 -> 6/12167}, {114.84 -> 1/12167}, {114.84 -> 2/12167}, {114.96 -> 6/12167}, {115.32 -> 4/12167}, {115.32 -> 2/12167}, {115.44 -> 18/12167}, {115.56 -> 6/12167}, {115.68 -> 6/12167}, {116.04 -> 6/12167}, {116.04 -> 5/12167}, {116.04 -> 4/12167}, {116.64 -> 2/12167}, {116.64 -> 4/12167}, {116.64 -> 6/12167}, {117.24 -> 1/12167}, {117.24 -> 2/12167}, {117.48 -> 6/12167}, {117.6 -> 6/12167}, {117.84 -> 3/12167}, {117.96 -> 3/12167}, {118.2 -> 4/12167}, {118.2 -> 2/12167}, {118.32 -> 6/12167}, {118.68 -> 6/12167}, {118.92 -> 2/12167}, {118.92 -> 2/12167}, {118.92 -> 2/12167}, {119.04 -> 4/12167}, {119.04 -> 2/12167}, {119.52 -> 2/12167}, {119.52 -> 14/12167}, {119.52 -> 2/12167}, {119.76 -> 6/12167}, {119.88 -> 3/12167}, {120.12 -> 12/12167}, {120.48 -> 6/12167}, {120.72 -> 6/12167}, {121.56 -> 6/12167}, {121.68 -> 6/12167}, {121.8 -> 1/12167}, {121.8 -> 2/12167}, {121.92 -> 4/12167}, {121.92 -> 2/12167}, {122.28 -> 4/12167}, {122.28 -> 2/12167}, {122.4 -> 6/12167}, {122.88 -> 4/12167}, {122.88 -> 2/12167}, {123.0 -> 18/12167}, {123.6 -> 6/12167}, {123.84 -> 6/12167}, {123.96 -> 2/12167}, {123.96 -> 4/12167}, {124.2 -> 2/12167}, {124.2 -> 1/12167}, {124.56 -> 7/12167}, {125.16 -> 9/12167}, {125.28 -> 6/12167}, {125.4 -> 6/12167}, {125.64 -> 3/12167}, {125.76 -> 3/12167}, {125.88 -> 3/12167}, {126.0 -> 4/12167}, {126.0 -> 2/12167}, {126.12 -> 1/12167}, {126.12 -> 2/12167}, {126.36 -> 1/12167}, {126.36 -> 2/12167}, {126.36 -> 10/12167}, {126.48 -> 2/12167}, {126.48 -> 10/12167}, {126.48 -> 6/12167}, {126.6 -> 4/12167}, {126.6 -> 2/12167}, {126.72 -> 3/12167}, {126.96 -> 6/12167}, {127.08 -> 4/12167}, {127.08 -> 4/12167}, {127.08 -> 4/12167}, {127.2 -> 4/12167}, {127.2 -> 2/12167}, {127.56 -> 6/12167}, {127.8 -> 4/12167}, {127.8 -> 2/12167}, {128.04 -> 8/12167}, {128.04 -> 4/12167}, {128.28 -> 6/12167}, {128.64 -> 18/12167}, {128.64 -> 9/12167}, {128.88 -> 9/12167}, {129.0 -> 3/12167}, {129.24 -> 18/12167}, {129.36 -> 2/12167}, {129.36 -> 4/12167}, {129.72 -> 6/12167}, {129.84 -> 3/12167}, {129.96 -> 3/12167}, {130.08 -> 2/12167}, {130.08 -> 10/12167}, {130.44 -> 6/12167}, {130.56 -> 18/12167}, {130.68 -> 6/12167}, {130.8 -> 6/12167}, {130.92 -> 6/12167}, {131.28 -> 6/12167}, {131.52 -> 4/12167}, {131.52 -> 5/12167}, {132.12 -> 18/12167}, {132.36 -> 4/12167}, {132.36 -> 2/12167}, {132.6 -> 3/12167}, {132.72 -> 16/12167}, {132.72 -> 2/12167}, {132.84 -> 3/12167}, {132.96 -> 2/12167}, {132.96 -> 4/12167}, {133.32 -> 9/12167}, {133.44 -> 6/12167}, {133.8 -> 3/12167}, {134.16 -> 12/12167}, {134.4 -> 3/12167}, {134.64 -> 6/12167}, {134.88 -> 10/12167}, {134.88 -> 2/12167}, {135.0 -> 27/12167}, {135.24 -> 4/12167}, {135.24 -> 2/12167}, {135.48 -> 6/12167}, {135.6 -> 18/12167}, {136.08 -> 1/12167}, {136.08 -> 2/12167}, {136.2 -> 9/12167}, {136.32 -> 6/12167}, {136.44 -> 6/12167}, {136.68 -> 3/12167}, {136.8 -> 7/12167}, {136.92 -> 3/12167}, {137.04 -> 6/12167}, {137.16 -> 6/12167}, {137.52 -> 4/12167}, {137.52 -> 2/12167}, {137.64 -> 6/12167}, {137.76 -> 6/12167}, {138.24 -> 6/12167}, {138.36 -> 3/12167}, {138.36 -> 12/12167}, {138.48 -> 11/12167}, {138.48 -> 4/12167}, {138.6 -> 10/12167}, {138.6 -> 5/12167}, {138.72 -> 6/12167}, {138.84 -> 4/12167}, {138.84 -> 2/12167}, {138.96 -> 12/12167}, {139.08 -> 13/12167}, {139.08 -> 14/12167}, {139.2 -> 2/12167}, {139.2 -> 4/12167}, {139.32 -> 6/12167}, {139.56 -> 6/12167}, {139.68 -> 21/12167}, {139.8 -> 4/12167}, {139.8 -> 5/12167}, {139.92 -> 4/12167}, {139.92 -> 8/12167}, {140.04 -> 3/12167}, {140.4 -> 6/12167}, {140.52 -> 6/12167}, {140.64 -> 12/12167}, {140.88 -> 9/12167}, {141.24 -> 15/12167}, {141.6 -> 3/12167}, {141.84 -> 12/12167}, {141.96 -> 9/12167}, {142.08 -> 8/12167}, {142.08 -> 4/12167}, {142.32 -> 18/12167}, {142.44 -> 6/12167}, {142.56 -> 9/12167}, {142.68 -> 12/12167}, {142.92 -> 4/12167}, {142.92 -> 2/12167}, {143.04 -> 2/12167}, {143.04 -> 1/12167}, {143.16 -> 15/12167}, {143.16 -> 12/12167}, {143.28 -> 6/12167}, {143.4 -> 2/12167}, {143.4 -> 10/12167}, {143.52 -> 6/12167}, {143.76 -> 12/12167}, {144.0 -> 12/12167}, {144.12 -> 15/12167}, {144.72 -> 6/12167}, {145.2 -> 6/12167}, {145.2 -> 3/12167}, {145.32 -> 5/12167}, {145.32 -> 4/12167}, {145.44 -> 10/12167}, {145.56 -> 6/12167}, {145.8 -> 3/12167}, {145.92 -> 4/12167}, {145.92 -> 8/12167}, {146.04 -> 13/12167}, {146.04 -> 14/12167}, {146.16 -> 6/12167}, {146.28 -> 2/12167}, {146.28 -> 4/12167}, {146.4 -> 2/12167}, {146.4 -> 4/12167}, {146.76 -> 3/12167}, {147.24 -> 12/12167}, {147.48 -> 6/12167}, {147.48 -> 6/12167}, {147.6 -> 10/12167}, {147.6 -> 2/12167}, {148.08 -> 2/12167}, {148.08 -> 4/12167}, {148.2 -> 12/12167}, {148.56 -> 6/12167}, {148.68 -> 6/12167}, {148.8 -> 2/12167}, {148.8 -> 1/12167}, {148.92 -> 3/12167}, {148.92 -> 6/12167}, {149.04 -> 6/12167}, {149.28 -> 2/12167}, {149.28 -> 7/12167}, {149.4 -> 18/12167}, {149.52 -> 14/12167}, {149.52 -> 13/12167}, {149.64 -> 14/12167}, {149.64 -> 4/12167}, {149.76 -> 9/12167}, {150.12 -> 15/12167}, {150.36 -> 9/12167}, {150.48 -> 4/12167}, {150.48 -> 2/12167}, {150.84 -> 4/12167}, {150.84 -> 5/12167}, {150.96 -> 3/12167}, {151.08 -> 3/12167}, {151.2 -> 2/12167}, {151.2 -> 4/12167}, {151.44 -> 6/12167}, {151.56 -> 6/12167}, {151.68 -> 24/12167}, {151.8 -> 6/12167}, {151.92 -> 4/12167}, {151.92 -> 11/12167}, {152.04 -> 3/12167}, {152.16 -> 3/12167}, {152.28 -> 24/12167}, {152.4 -> 3/12167}, {152.52 -> 5/12167}, {152.52 -> 10/12167}, {152.64 -> 12/12167}, {152.64 -> 3/12167}, {152.76 -> 6/12167}, {152.88 -> 6/12167}, {153.0 -> 6/12167}, {153.12 -> 27/12167}, {153.24 -> 3/12167}, {153.36 -> 6/12167}, {153.48 -> 3/12167}, {153.48 -> 12/12167}, {153.6 -> 8/12167}, {153.6 -> 4/12167}, {153.72 -> 6/12167}, {153.84 -> 15/12167}, {153.96 -> 6/12167}, {154.32 -> 12/12167}, {154.44 -> 6/12167}, {154.56 -> 18/12167}, {154.92 -> 6/12167}, {154.92 -> 6/12167}, {155.04 -> 6/12167}, {155.16 -> 16/12167}, {155.16 -> 2/12167}, {155.28 -> 6/12167}, {155.4 -> 12/12167}, {155.52 -> 4/12167}, {155.52 -> 3/12167}, {155.64 -> 3/12167}, {155.64 -> 3/12167}, {155.76 -> 21/12167}, {155.76 -> 6/12167}, {155.88 -> 7/12167}, {156.0 -> 24/12167}, {156.12 -> 6/12167}, {156.36 -> 4/12167}, {156.36 -> 14/12167}, {156.48 -> 3/12167}, {156.6 -> 10/12167}, {156.6 -> 2/12167}, {156.72 -> 12/12167}, {157.2 -> 12/12167}, {157.44 -> 6/12167}, {157.56 -> 6/12167}, {157.8 -> 2/12167}, {157.8 -> 7/12167}, {157.92 -> 6/12167}, {158.04 -> 7/12167}, {158.04 -> 2/12167}, {158.16 -> 6/12167}, {158.4 -> 4/12167}, {158.4 -> 2/12167}, {158.64 -> 16/12167}, {158.64 -> 14/12167}, {158.88 -> 6/12167}, {159.0 -> 3/12167}, {159.12 -> 3/12167}, {159.24 -> 4/12167}, {159.24 -> 17/12167}, {159.36 -> 6/12167}, {159.48 -> 10/12167}, {159.48 -> 5/12167}, {159.6 -> 3/12167}, {159.84 -> 6/12167}, {160.08 -> 4/12167}, {160.08 -> 2/12167}, {160.2 -> 3/12167}, {160.56 -> 6/12167}, {161.16 -> 4/12167}, {161.16 -> 2/12167}, {161.28 -> 6/12167}, {161.52 -> 2/12167}, {161.52 -> 10/12167}, {161.64 -> 2/12167}, {161.64 -> 4/12167}, {161.76 -> 6/12167}, {161.88 -> 12/12167}, {162.0 -> 12/12167}, {162.12 -> 18/12167}, {162.24 -> 6/12167}, {162.36 -> 1/12167}, {162.36 -> 6/12167}, {162.6 -> 8/12167}, {162.6 -> 4/12167}, {162.72 -> 30/12167}, {162.84 -> 12/12167}, {162.96 -> 8/12167}, {162.96 -> 14/12167}, {162.96 -> 2/12167}, {163.08 -> 3/12167}, {163.44 -> 6/12167}, {163.56 -> 6/12167}, {163.68 -> 6/12167}, {163.8 -> 3/12167}, {163.8 -> 3/12167}, {164.04 -> 6/12167}, {164.16 -> 4/12167}, {164.16 -> 2/12167}, {164.28 -> 12/12167}, {164.52 -> 5/12167}, {164.52 -> 10/12167}, {164.64 -> 3/12167}, {164.76 -> 3/12167}, {164.88 -> 24/12167}, {165.0 -> 12/12167}, {165.12 -> 18/12167}, {165.24 -> 15/12167}, {165.36 -> 2/12167}, {165.36 -> 16/12167}, {165.48 -> 4/12167}, {165.48 -> 2/12167}, {165.6 -> 16/12167}, {165.6 -> 2/12167}, {165.72 -> 8/12167}, {165.72 -> 4/12167}, {165.84 -> 3/12167}, {165.84 -> 6/12167}, {165.96 -> 6/12167}, {166.08 -> 4/12167}, {166.08 -> 8/12167}, {166.2 -> 20/12167}, {166.2 -> 4/12167}, {166.32 -> 18/12167}, {166.44 -> 18/12167}, {166.56 -> 12/12167}, {166.68 -> 4/12167}, {167.04 -> 6/12167}, {167.16 -> 4/12167}, {167.16 -> 5/12167}, {167.52 -> 4/12167}, {167.52 -> 2/12167}, {167.64 -> 2/12167}, {167.64 -> 10/12167}, {167.76 -> 8/12167}, {167.76 -> 4/12167}, {168.12 -> 6/12167}, {168.24 -> 2/12167}, {168.24 -> 10/12167}, {168.36 -> 4/12167}, {168.36 -> 17/12167}, {168.48 -> 4/12167}, {168.48 -> 2/12167}, {168.6 -> 13/12167}, {168.6 -> 8/12167}, {168.96 -> 6/12167}, {168.96 -> 18/12167}, {169.08 -> 12/12167}, {169.08 -> 12/12167}, {169.2 -> 6/12167}, {169.32 -> 12/12167}, {169.44 -> 12/12167}, {169.68 -> 12/12167}, {169.8 -> 18/12167}, {170.04 -> 6/12167}, {170.28 -> 12/12167}, {170.4 -> 4/12167}, {170.4 -> 2/12167}, {170.52 -> 14/12167}, {170.52 -> 4/12167}, {170.64 -> 18/12167}, {170.76 -> 3/12167}, {170.88 -> 6/12167}, {171.12 -> 3/12167}, {171.24 -> 4/12167}, {171.24 -> 20/12167}, {171.48 -> 10/12167}, {171.48 -> 5/12167}, {171.6 -> 4/12167}, {171.6 -> 2/12167}, {171.72 -> 9/12167}, {171.84 -> 2/12167}, {171.84 -> 13/12167}, {172.08 -> 6/12167}, {172.2 -> 6/12167}, {172.32 -> 6/12167}, {172.44 -> 12/12167}, {172.56 -> 9/12167}, {172.68 -> 24/12167}, {172.8 -> 3/12167}, {172.92 -> 6/12167}, {173.16 -> 6/12167}, {173.16 -> 6/12167}, {173.76 -> 12/12167}, {173.88 -> 12/12167}, {174.0 -> 6/12167}, {174.12 -> 6/12167}, {174.6 -> 14/12167}, {174.6 -> 4/12167}, {174.72 -> 22/12167}, {174.72 -> 2/12167}, {174.84 -> 6/12167}, {174.84 -> 12/12167}, {174.96 -> 2/12167}, {174.96 -> 10/12167}, {175.2 -> 6/12167}, {175.32 -> 9/12167}, {175.56 -> 10/12167}, {175.56 -> 2/12167}, {175.68 -> 6/12167}, {176.04 -> 5/12167}, {176.04 -> 16/12167}, {176.16 -> 14/12167}, {176.16 -> 13/12167}, {176.28 -> 10/12167}, {176.28 -> 2/12167}, {176.4 -> 6/12167}, {176.76 -> 2/12167}, {176.76 -> 4/12167}, {176.88 -> 12/12167}, {177.12 -> 12/12167}, {177.24 -> 2/12167}, {177.24 -> 4/12167}, {177.36 -> 3/12167}, {177.48 -> 4/12167}, {177.48 -> 8/12167}, {177.6 -> 12/12167}, {177.72 -> 2/12167}, {177.72 -> 1/12167}, {177.84 -> 6/12167}, {177.96 -> 8/12167}, {177.96 -> 10/12167}, {178.08 -> 12/12167}, {178.2 -> 12/12167}, {178.2 -> 6/12167}, {178.32 -> 12/12167}, {178.56 -> 24/12167}, {178.8 -> 2/12167}, {178.8 -> 28/12167}, {178.92 -> 6/12167}, {178.92 -> 3/12167}, {179.04 -> 8/12167}, {179.04 -> 4/12167}, {179.28 -> 9/12167}, {179.4 -> 8/12167}, {179.4 -> 8/12167}, {179.4 -> 2/12167}, {179.52 -> 4/12167}, {179.52 -> 2/12167}, {179.64 -> 26/12167}, {179.64 -> 10/12167}, {179.76 -> 8/12167}, {179.76 -> 4/12167}, {179.88 -> 9/12167}, {180.0 -> 3/12167}, {180.12 -> 2/12167}, {180.12 -> 4/12167}, {180.24 -> 18/12167}, {180.36 -> 2/12167}, {180.36 -> 16/12167}, {180.84 -> 10/12167}, {180.84 -> 2/12167}, {180.96 -> 6/12167}, {181.08 -> 3/12167}, {181.2 -> 3/12167}, {181.2 -> 6/12167}, {181.56 -> 6/12167}, {181.68 -> 33/12167}, {181.8 -> 6/12167}, {181.92 -> 6/12167}, {182.04 -> 4/12167}, {182.04 -> 8/12167}, {182.28 -> 2/12167}, {182.28 -> 10/12167}, {182.52 -> 2/12167}, {182.52 -> 4/12167}, {182.88 -> 15/12167}, {183.12 -> 4/12167}, {183.12 -> 20/12167}, {183.24 -> 2/12167}, {183.24 -> 4/12167}, {183.36 -> 3/12167}, {183.48 -> 2/12167}, {183.48 -> 4/12167}, {183.6 -> 4/12167}, {183.6 -> 2/12167}, {183.72 -> 12/12167}, {183.84 -> 6/12167}, {184.08 -> 3/12167}, {184.32 -> 9/12167}, {184.44 -> 12/12167}, {184.56 -> 6/12167}, {184.92 -> 4/12167}, {184.92 -> 14/12167}, {185.16 -> 2/12167}, {185.16 -> 16/12167}, {185.28 -> 6/12167}, {185.4 -> 6/12167}, {185.76 -> 37/12167}, {185.76 -> 2/12167}, {185.88 -> 7/12167}, {185.88 -> 2/12167}, {186.0 -> 4/12167}, {186.0 -> 18/12167}, {186.0 -> 2/12167}, {186.12 -> 3/12167}, {186.24 -> 3/12167}, {186.36 -> 2/12167}, {186.36 -> 4/12167}, {186.48 -> 6/12167}, {186.6 -> 8/12167}, {186.6 -> 10/12167}, {186.72 -> 10/12167}, {186.72 -> 2/12167}, {187.08 -> 6/12167}, {187.2 -> 14/12167}, {187.2 -> 4/12167}, {187.32 -> 10/12167}, {187.32 -> 2/12167}, {187.44 -> 9/12167}, {187.56 -> 3/12167}, {187.8 -> 3/12167}, {187.92 -> 2/12167}, {187.92 -> 10/12167}, {188.04 -> 6/12167}, {188.04 -> 3/12167}, {188.16 -> 8/12167}, {188.16 -> 7/12167}, {188.28 -> 12/12167}, {188.4 -> 8/12167}, {188.4 -> 4/12167}, {188.52 -> 4/12167}, {188.52 -> 2/12167}, {188.64 -> 8/12167}, {188.64 -> 4/12167}, {188.76 -> 4/12167}, {188.76 -> 8/12167}, {188.88 -> 7/12167}, {188.88 -> 2/12167}, {189.12 -> 12/12167}, {189.24 -> 2/12167}, {189.24 -> 16/12167}, {189.36 -> 4/12167}, {189.36 -> 17/12167}, {189.48 -> 8/12167}, {189.48 -> 10/12167}, {189.6 -> 3/12167}, {189.6 -> 6/12167}, {189.72 -> 2/12167}, {189.72 -> 4/12167}, {189.84 -> 11/12167}, {189.84 -> 4/12167}, {189.96 -> 6/12167}, {189.96 -> 6/12167}, {190.08 -> 4/12167}, {190.08 -> 14/12167}, {190.2 -> 2/12167}, {190.2 -> 10/12167}, {190.32 -> 6/12167}, {190.56 -> 18/12167}, {190.68 -> 24/12167}, {190.8 -> 2/12167}, {190.8 -> 22/12167}, {190.92 -> 6/12167}, {191.16 -> 3/12167}, {191.4 -> 8/12167}, {191.4 -> 10/12167}, {191.52 -> 12/12167}, {191.52 -> 6/12167}, {191.64 -> 24/12167}, {191.64 -> 6/12167}, {191.88 -> 9/12167}, {192.0 -> 16/12167}, {192.0 -> 2/12167}, {192.12 -> 6/12167}, {192.24 -> 18/12167}, {192.36 -> 15/12167}, {192.6 -> 8/12167}, {192.6 -> 4/12167}, {192.72 -> 12/12167}, {192.84 -> 24/12167}, {192.96 -> 12/12167}, {193.08 -> 12/12167}, {193.32 -> 3/12167}, {193.44 -> 10/12167}, {193.44 -> 2/12167}, {193.56 -> 12/12167}, {193.68 -> 6/12167}, {193.8 -> 6/12167}, {193.92 -> 9/12167}, {194.04 -> 5/12167}, {194.04 -> 4/12167}, {194.28 -> 26/12167}, {194.28 -> 4/12167}, {194.4 -> 6/12167}, {194.4 -> 6/12167}, {194.52 -> 6/12167}, {194.76 -> 12/12167}, {194.88 -> 18/12167}, {195.0 -> 6/12167}, {195.12 -> 18/12167}, {195.24 -> 3/12167}, {195.36 -> 6/12167}, {195.6 -> 3/12167}, {195.72 -> 16/12167}, {195.72 -> 2/12167}, {195.84 -> 6/12167}, {196.08 -> 2/12167}, {196.08 -> 4/12167}, {196.2 -> 16/12167}, {196.2 -> 2/12167}, {196.32 -> 9/12167}, {196.44 -> 12/12167}, {196.8 -> 3/12167}, {196.92 -> 6/12167}, {197.04 -> 2/12167}, {197.04 -> 4/12167}, {197.16 -> 6/12167}, {197.16 -> 3/12167}, {197.52 -> 2/12167}, {197.52 -> 4/12167}, {197.64 -> 4/12167}, {197.64 -> 2/12167}, {197.76 -> 10/12167}, {197.76 -> 2/12167}, {197.88 -> 6/12167}, {198.36 -> 6/12167}, {198.36 -> 18/12167}, {198.48 -> 4/12167}, {198.48 -> 8/12167}, {198.6 -> 6/12167}, {198.6 -> 6/12167}, {198.96 -> 6/12167}, {198.96 -> 6/12167}, {199.08 -> 10/12167}, {199.08 -> 14/12167}, {199.2 -> 10/12167}, {199.2 -> 14/12167}, {199.32 -> 2/12167}, {199.32 -> 4/12167}, {199.44 -> 6/12167}, {199.8 -> 2/12167}, {199.8 -> 10/12167}, {199.92 -> 6/12167}, {199.92 -> 12/12167}, {200.04 -> 6/12167}, {200.28 -> 4/12167}, {200.28 -> 8/12167}, {200.4 -> 2/12167}, {200.4 -> 4/12167}, {200.52 -> 6/12167}, {200.52 -> 6/12167}, {200.64 -> 6/12167}, {200.64 -> 6/12167}, {200.76 -> 2/12167}, {200.76 -> 4/12167}, {201.24 -> 6/12167}, {201.24 -> 15/12167}, {201.36 -> 15/12167}, {201.48 -> 12/12167}, {201.48 -> 6/12167}, {201.84 -> 2/12167}, {201.84 -> 4/12167}, {202.08 -> 5/12167}, {202.08 -> 4/12167}, {202.2 -> 6/12167}, {202.32 -> 1/12167}, {202.32 -> 2/12167}, {202.44 -> 18/12167}, {202.44 -> 6/12167}, {202.56 -> 2/12167}, {202.56 -> 25/12167}, {202.68 -> 2/12167}, {202.68 -> 22/12167}, {202.8 -> 2/12167}, {202.8 -> 13/12167}, {202.92 -> 12/12167}, {203.04 -> 4/12167}, {203.04 -> 8/12167}, {203.16 -> 6/12167}, {203.28 -> 14/12167}, {203.28 -> 4/12167}, {203.4 -> 5/12167}, {203.4 -> 10/12167}, {203.4 -> 4/12167}, {203.52 -> 12/12167}, {203.64 -> 6/12167}, {203.76 -> 4/12167}, {203.76 -> 2/12167}, {203.88 -> 16/12167}, {203.88 -> 2/12167}, {204.12 -> 9/12167}, {204.24 -> 9/12167}, {204.48 -> 1/12167}, {204.48 -> 2/12167}, {204.6 -> 6/12167}, {204.6 -> 12/12167}, {204.72 -> 14/12167}, {204.72 -> 4/12167}, {204.84 -> 12/12167}, {204.96 -> 6/12167}, {205.08 -> 12/12167}, {205.32 -> 18/12167}, {205.44 -> 2/12167}, {205.44 -> 10/12167}, {205.56 -> 15/12167}, {205.92 -> 14/12167}, {206.04 -> 4/12167}, {206.04 -> 8/12167}, {206.16 -> 8/12167}, {206.16 -> 14/12167}, {206.16 -> 8/12167}, {206.28 -> 12/12167}, {206.4 -> 6/12167}, {206.52 -> 4/12167}, {206.52 -> 8/12167}, {206.64 -> 13/12167}, {206.76 -> 12/12167}, {206.88 -> 15/12167}, {207.0 -> 12/12167}, {207.12 -> 12/12167}, {207.36 -> 4/12167}, {207.36 -> 8/12167}, {207.48 -> 18/12167}, {207.6 -> 6/12167}, {207.72 -> 12/12167}, {207.84 -> 6/12167}, {207.96 -> 4/12167}, {207.96 -> 2/12167}, {208.32 -> 18/12167}, {208.44 -> 6/12167}, {208.56 -> 12/12167}, {208.68 -> 6/12167}, {208.8 -> 2/12167}, {208.8 -> 25/12167}, {208.92 -> 4/12167}, {208.92 -> 8/12167}, {209.04 -> 4/12167}, {209.04 -> 5/12167}, {209.16 -> 9/12167}, {209.4 -> 12/12167}, {209.4 -> 12/12167}, {209.52 -> 6/12167}, {209.52 -> 3/12167}, {209.64 -> 12/12167}, {209.64 -> 6/12167}, {209.76 -> 4/12167}, {209.76 -> 5/12167}, {209.88 -> 6/12167}, {210.24 -> 4/12167}, {210.24 -> 14/12167}, {210.36 -> 3/12167}, {210.48 -> 6/12167}, {210.96 -> 4/12167}, {210.96 -> 5/12167}, {211.08 -> 7/12167}, {211.08 -> 8/12167}, {211.2 -> 2/12167}, {211.2 -> 4/12167}, {211.56 -> 6/12167}, {211.68 -> 12/12167}, {211.8 -> 6/12167}, {211.92 -> 6/12167}, {212.04 -> 2/12167}, {212.04 -> 4/12167}, {212.16 -> 3/12167}, {212.28 -> 1/12167}, {212.28 -> 2/12167}, {212.4 -> 4/12167}, {212.4 -> 2/12167}, {212.52 -> 6/12167}, {212.52 -> 6/12167}, {212.64 -> 6/12167}, {212.76 -> 8/12167}, {212.76 -> 4/12167}, {212.88 -> 26/12167}, {212.88 -> 4/12167}, {213.0 -> 6/12167}, {213.12 -> 2/12167}, {213.12 -> 4/12167}, {213.24 -> 6/12167}, {213.36 -> 9/12167}, {213.6 -> 8/12167}, {213.6 -> 10/12167}, {213.72 -> 6/12167}, {213.72 -> 8/12167}, {213.72 -> 4/12167}, {213.84 -> 9/12167}, {213.96 -> 6/12167}, {214.08 -> 1/12167}, {214.08 -> 2/12167}, {214.44 -> 16/12167}, {214.44 -> 2/12167}, {214.56 -> 12/12167}, {214.68 -> 6/12167}, {214.8 -> 6/12167}, {214.8 -> 6/12167}, {214.92 -> 2/12167}, {214.92 -> 4/12167}, {215.04 -> 8/12167}, {215.04 -> 16/12167}, {215.16 -> 19/12167}, {215.16 -> 5/12167}, {215.28 -> 8/12167}, {215.28 -> 4/12167}, {215.52 -> 12/12167}, {215.64 -> 4/12167}, {215.64 -> 2/12167}, {215.76 -> 30/12167}, {215.88 -> 24/12167}, {216.0 -> 2/12167}, {216.0 -> 12/12167}, {216.0 -> 4/12167}, {216.12 -> 18/12167}, {216.24 -> 9/12167}, {216.48 -> 12/12167}, {216.6 -> 10/12167}, {216.6 -> 8/12167}, {216.72 -> 3/12167}, {216.84 -> 12/12167}, {216.96 -> 3/12167}, {217.32 -> 12/12167}, {217.56 -> 6/12167}, {217.92 -> 2/12167}, {217.92 -> 4/12167}, {218.04 -> 6/12167}, {218.16 -> 6/12167}, {218.28 -> 4/12167}, {218.28 -> 2/12167}, {218.4 -> 4/12167}, {218.4 -> 2/12167}, {218.52 -> 6/12167}, {218.52 -> 6/12167}, {218.64 -> 6/12167}, {218.76 -> 6/12167}, {218.88 -> 6/12167}, {219.12 -> 15/12167}, {219.24 -> 4/12167}, {219.24 -> 20/12167}, {219.36 -> 6/12167}, {219.36 -> 18/12167}, {219.48 -> 4/12167}, {219.48 -> 2/12167}, {219.6 -> 6/12167}, {219.72 -> 1/12167}, {219.72 -> 2/12167}, {220.08 -> 4/12167}, {220.08 -> 11/12167}, {220.2 -> 6/12167}, {220.2 -> 3/12167}, {220.32 -> 6/12167}, {220.56 -> 18/12167}, {220.68 -> 6/12167}, {220.8 -> 6/12167}, {221.28 -> 4/12167}, {221.28 -> 2/12167}, {221.4 -> 18/12167}, {221.4 -> 24/12167}, {221.52 -> 2/12167}, {221.52 -> 4/12167}, {221.64 -> 24/12167}, {221.88 -> 9/12167}, {222.0 -> 24/12167}, {222.12 -> 6/12167}, {222.12 -> 12/12167}, {222.24 -> 4/12167}, {222.24 -> 14/12167}, {222.36 -> 9/12167}, {222.48 -> 6/12167}, {222.84 -> 4/12167}, {222.84 -> 14/12167}, {222.96 -> 4/12167}, {222.96 -> 14/12167}, {223.08 -> 6/12167}, {223.2 -> 6/12167}, {223.56 -> 6/12167}, {223.68 -> 6/12167}, {223.8 -> 3/12167}, {224.16 -> 6/12167}, {224.28 -> 2/12167}, {224.28 -> 14/12167}, {224.28 -> 2/12167}, {224.64 -> 6/12167}, {224.76 -> 16/12167}, {224.76 -> 2/12167}, {224.88 -> 13/12167}, {224.88 -> 2/12167}, {225.0 -> 2/12167}, {225.0 -> 5/12167}, {225.0 -> 2/12167}, {225.12 -> 6/12167}, {225.36 -> 2/12167}, {225.36 -> 4/12167}, {225.48 -> 10/12167}, {225.48 -> 20/12167}, {225.6 -> 4/12167}, {225.6 -> 20/12167}, {225.6 -> 18/12167}, {225.72 -> 24/12167}, {225.72 -> 6/12167}, {225.84 -> 6/12167}, {225.84 -> 6/12167}, {225.96 -> 6/12167}, {226.2 -> 3/12167}, {226.32 -> 8/12167}, {226.32 -> 4/12167}, {226.44 -> 8/12167}, {226.44 -> 4/12167}, {226.56 -> 6/12167}, {226.68 -> 6/12167}, {227.04 -> 2/12167}, {227.04 -> 4/12167}, {227.16 -> 6/12167}, {227.64 -> 4/12167}, {227.64 -> 2/12167}, {227.76 -> 12/12167}, {227.76 -> 3/12167}, {227.88 -> 18/12167}, {228.12 -> 9/12167}, {228.24 -> 2/12167}, {228.24 -> 4/12167}, {228.36 -> 10/12167}, {228.36 -> 11/12167}, {228.48 -> 6/12167}, {228.48 -> 6/12167}, {228.6 -> 4/12167}, {228.6 -> 8/12167}, {228.72 -> 5/12167}, {228.72 -> 4/12167}, {228.84 -> 6/12167}, {228.84 -> 12/12167}, {229.08 -> 2/12167}, {229.08 -> 10/12167}, {229.2 -> 12/12167}, {229.2 -> 6/12167}, {229.32 -> 12/12167}, {229.56 -> 33/12167}, {229.68 -> 12/12167}, {229.8 -> 12/12167}, {229.92 -> 6/12167}, {229.92 -> 6/12167}, {230.04 -> 6/12167}, {230.04 -> 12/12167}, {230.28 -> 2/12167}, {230.28 -> 7/12167}, {230.4 -> 8/12167}, {230.4 -> 4/12167}, {230.52 -> 4/12167}, {230.52 -> 2/12167}, {230.64 -> 18/12167}, {230.76 -> 6/12167}, {230.88 -> 3/12167}, {231.24 -> 2/12167}, {231.24 -> 13/12167}, {231.36 -> 12/12167}, {231.48 -> 6/12167}, {231.6 -> 2/12167}, {231.6 -> 1/12167}, {231.72 -> 7/12167}, {231.72 -> 2/12167}, {231.84 -> 12/12167}, {231.96 -> 3/12167}, {231.96 -> 12/12167}, {232.08 -> 6/12167}, {232.08 -> 6/12167}, {232.68 -> 6/12167}, {232.8 -> 12/12167}, {233.28 -> 4/12167}, {233.28 -> 2/12167}, {233.4 -> 2/12167}, {233.4 -> 8/12167}, {233.4 -> 2/12167}, {233.88 -> 12/12167}, {234.0 -> 12/12167}, {234.12 -> 6/12167}, {234.24 -> 3/12167}, {234.6 -> 2/12167}, {234.6 -> 4/12167}, {234.72 -> 7/12167}, {234.72 -> 2/12167}, {234.84 -> 6/12167}, {235.08 -> 12/12167}, {235.32 -> 16/12167}, {235.32 -> 2/12167}, {235.44 -> 10/12167}, {235.44 -> 2/12167}, {235.56 -> 12/12167}, {235.92 -> 12/12167}, {236.04 -> 3/12167}, {236.16 -> 8/12167}, {236.16 -> 7/12167}, {236.28 -> 1/12167}, {236.28 -> 2/12167}, {236.4 -> 3/12167}, {236.76 -> 6/12167}, {236.88 -> 18/12167}, {237.12 -> 3/12167}, {237.24 -> 6/12167}, {237.36 -> 6/12167}, {237.36 -> 6/12167}, {237.48 -> 2/12167}, {237.48 -> 4/12167}, {237.6 -> 2/12167}, {237.6 -> 4/12167}, {237.72 -> 12/12167}, {237.84 -> 4/12167}, {237.84 -> 2/12167}, {237.96 -> 6/12167}, {238.08 -> 8/12167}, {238.08 -> 7/12167}, {238.2 -> 8/12167}, {238.2 -> 7/12167}, {238.32 -> 10/12167}, {238.32 -> 2/12167}, {238.44 -> 12/12167}, {238.68 -> 12/12167}, {238.8 -> 4/12167}, {238.8 -> 11/12167}, {238.92 -> 2/12167}, {238.92 -> 10/12167}, {239.04 -> 12/12167}, {239.04 -> 3/12167}, {239.16 -> 3/12167}, {239.16 -> 3/12167}, {239.4 -> 2/12167}, {239.4 -> 4/12167}, {239.76 -> 6/12167}, {239.76 -> 6/12167}, {239.88 -> 4/12167}, {239.88 -> 2/12167}, {240.24 -> 2/12167}, {240.24 -> 4/12167}, {240.36 -> 9/12167}, {240.48 -> 6/12167}, {240.6 -> 2/12167}, {240.6 -> 1/12167}, {240.72 -> 1/12167}, {240.72 -> 2/12167}, {240.96 -> 4/12167}, {240.96 -> 2/12167}, {241.08 -> 6/12167}, {241.08 -> 12/12167}, {241.2 -> 6/12167}, {241.32 -> 6/12167}, {241.44 -> 2/12167}, {241.44 -> 7/12167}, {241.56 -> 12/12167}, {241.8 -> 15/12167}, {241.92 -> 6/12167}, {242.16 -> 4/12167}, {242.16 -> 8/12167}, {242.28 -> 8/12167}, {242.28 -> 12/12167}, {242.28 -> 4/12167}, {242.4 -> 10/12167}, {242.4 -> 8/12167}, {242.52 -> 10/12167}, {242.52 -> 2/12167}, {242.64 -> 12/12167}, {242.88 -> 6/12167}, {243.12 -> 18/12167}, {243.24 -> 9/12167}, {243.36 -> 4/12167}, {243.36 -> 14/12167}, {243.6 -> 5/12167}, {243.6 -> 4/12167}, {243.72 -> 4/12167}, {243.72 -> 2/12167}, {243.84 -> 10/12167}, {243.84 -> 2/12167}, {243.96 -> 6/12167}, {244.08 -> 6/12167}, {244.2 -> 6/12167}, {244.32 -> 2/12167}, {244.32 -> 4/12167}, {244.44 -> 12/12167}, {244.56 -> 12/12167}, {244.68 -> 3/12167}, {244.8 -> 6/12167}, {245.04 -> 4/12167}, {245.04 -> 20/12167}, {245.16 -> 4/12167}, {245.16 -> 14/12167}, {245.28 -> 2/12167}, {245.28 -> 8/12167}, {245.28 -> 2/12167}, {245.4 -> 6/12167}, {245.4 -> 6/12167}, {245.52 -> 6/12167}, {245.76 -> 3/12167}, {245.88 -> 24/12167}, {246.0 -> 4/12167}, {246.0 -> 2/12167}, {246.12 -> 6/12167}, {246.6 -> 2/12167}, {246.6 -> 4/12167}, {246.72 -> 6/12167}, {246.84 -> 6/12167}, {247.32 -> 6/12167}, {247.44 -> 6/12167}, {247.56 -> 6/12167}, {247.68 -> 2/12167}, {247.68 -> 10/12167}, {247.8 -> 4/12167}, {247.8 -> 2/12167}, {247.92 -> 2/12167}, {247.92 -> 10/12167}, {248.4 -> 4/12167}, {248.4 -> 8/12167}, {248.52 -> 16/12167}, {248.52 -> 14/12167}, {248.64 -> 12/12167}, {248.64 -> 6/12167}, {248.76 -> 10/12167}, {248.76 -> 2/12167}, {248.88 -> 6/12167}, {249.12 -> 3/12167}, {249.24 -> 3/12167}, {249.36 -> 2/12167}, {249.36 -> 4/12167}, {249.84 -> 4/12167}, {249.84 -> 2/12167}, {249.96 -> 6/12167}, {249.96 -> 4/12167}, {249.96 -> 2/12167}, {250.08 -> 8/12167}, {250.08 -> 10/12167}, {250.2 -> 6/12167}, {250.56 -> 6/12167}, {250.68 -> 12/12167}, {250.8 -> 6/12167}, {250.8 -> 18/12167}, {250.92 -> 2/12167}, {250.92 -> 16/12167}, {251.04 -> 12/12167}, {251.28 -> 4/12167}, {251.28 -> 2/12167}, {251.4 -> 16/12167}, {251.4 -> 5/12167}, {251.64 -> 10/12167}, {251.64 -> 2/12167}, {251.76 -> 6/12167}, {251.76 -> 3/12167}, {252.0 -> 6/12167}, {252.12 -> 12/12167}, {252.24 -> 2/12167}, {252.24 -> 16/12167}, {252.36 -> 16/12167}, {252.48 -> 6/12167}, {252.48 -> 6/12167}, {252.84 -> 2/12167}, {252.84 -> 1/12167}, {252.96 -> 2/12167}, {252.96 -> 4/12167}, {253.08 -> 12/12167}, {253.2 -> 3/12167}, {253.56 -> 4/12167}, {253.56 -> 2/12167}, {253.68 -> 6/12167}, {253.8 -> 9/12167}, {254.04 -> 9/12167}, {254.16 -> 10/12167}, {254.16 -> 8/12167}, {254.28 -> 10/12167}, {254.28 -> 2/12167}, {254.52 -> 6/12167}, {254.88 -> 12/12167}, {255.12 -> 3/12167}, {255.48 -> 6/12167}, {255.6 -> 2/12167}, {255.6 -> 4/12167}, {255.6 -> 6/12167}, {255.72 -> 4/12167}, {255.72 -> 2/12167}, {255.84 -> 3/12167}, {256.32 -> 2/12167}, {256.32 -> 4/12167}, {256.44 -> 15/12167}, {256.56 -> 6/12167}, {257.04 -> 12/12167}, {257.28 -> 2/12167}, {257.28 -> 1/12167}, {257.64 -> 7/12167}, {257.64 -> 2/12167}, {257.76 -> 12/12167}, {257.88 -> 24/12167}, {258.12 -> 6/12167}, {258.24 -> 6/12167}, {258.36 -> 6/12167}, {258.6 -> 18/12167}, {258.72 -> 3/12167}, {258.84 -> 6/12167}, {259.08 -> 6/12167}, {259.32 -> 6/12167}, {259.44 -> 6/12167}, {259.56 -> 12/12167}, {259.68 -> 2/12167}, {259.68 -> 4/12167}, {259.92 -> 12/12167}, {260.04 -> 2/12167}, {260.04 -> 4/12167}, {260.16 -> 6/12167}, {260.16 -> 3/12167}, {260.4 -> 12/12167}, {260.52 -> 14/12167}, {260.52 -> 4/12167}, {260.64 -> 12/12167}, {261.12 -> 6/12167}, {261.36 -> 3/12167}, {261.96 -> 12/12167}, {262.08 -> 4/12167}, {262.08 -> 5/12167}, {262.2 -> 1/12167}, {262.2 -> 2/12167}, {262.56 -> 6/12167}, {262.68 -> 12/12167}, {262.8 -> 4/12167}, {262.8 -> 8/12167}, {262.92 -> 6/12167}, {263.16 -> 2/12167}, {263.16 -> 4/12167}, {263.28 -> 6/12167}, {263.4 -> 4/12167}, {263.4 -> 2/12167}, {263.52 -> 6/12167}, {263.64 -> 6/12167}, {263.88 -> 6/12167}, {264.0 -> 18/12167}, {264.12 -> 6/12167}, {264.36 -> 15/12167}, {264.48 -> 4/12167}, {264.48 -> 8/12167}, {264.6 -> 9/12167}, {264.72 -> 4/12167}, {264.72 -> 2/12167}, {265.08 -> 5/12167}, {265.08 -> 4/12167}, {265.2 -> 12/12167}, {265.32 -> 12/12167}, {265.44 -> 12/12167}, {265.56 -> 4/12167}, {265.56 -> 8/12167}, {265.68 -> 3/12167}, {265.8 -> 3/12167}, {265.8 -> 6/12167}, {265.92 -> 6/12167}, {266.04 -> 12/12167}, {266.16 -> 11/12167}, {266.16 -> 4/12167}, {266.28 -> 6/12167}, {266.52 -> 6/12167}, {266.64 -> 4/12167}, {266.64 -> 2/12167}, {266.76 -> 24/12167}, {266.88 -> 27/12167}, {267.12 -> 6/12167}, {267.24 -> 3/12167}, {267.36 -> 6/12167}, {267.48 -> 12/12167}, {267.6 -> 18/12167}, {267.72 -> 6/12167}, {267.84 -> 6/12167}, {268.08 -> 6/12167}, {268.2 -> 6/12167}, {268.68 -> 6/12167}, {268.8 -> 2/12167}, {268.8 -> 4/12167}, {269.04 -> 6/12167}, {269.52 -> 4/12167}, {269.52 -> 2/12167}, {269.64 -> 12/12167}, {270.12 -> 6/12167}, {270.36 -> 6/12167}, {270.48 -> 6/12167}, {270.84 -> 6/12167}, {270.96 -> 6/12167}, {270.96 -> 12/12167}, {271.08 -> 2/12167}, {271.08 -> 4/12167}, {271.2 -> 6/12167}, {271.56 -> 6/12167}, {272.16 -> 6/12167}, {272.28 -> 8/12167}, {272.28 -> 4/12167}, {272.4 -> 12/12167}, {272.64 -> 6/12167}, {272.88 -> 6/12167}, {273.0 -> 12/12167}, {273.12 -> 24/12167}, {273.36 -> 9/12167}, {273.72 -> 9/12167}, {273.84 -> 6/12167}, {273.84 -> 6/12167}, {273.96 -> 3/12167}, {274.08 -> 3/12167}, {274.2 -> 6/12167}, {274.56 -> 12/12167}, {274.68 -> 6/12167}, {275.04 -> 18/12167}, {275.16 -> 8/12167}, {275.16 -> 10/12167}, {275.28 -> 22/12167}, {275.28 -> 2/12167}, {275.4 -> 12/12167}, {275.88 -> 12/12167}, {276.0 -> 12/12167}, {276.6 -> 6/12167}, {276.72 -> 6/12167}, {277.08 -> 3/12167}, {277.2 -> 2/12167}, {277.2 -> 4/12167}, {277.32 -> 3/12167}, {277.44 -> 6/12167}, {278.04 -> 3/12167}, {278.4 -> 4/12167}, {278.4 -> 2/12167}, {278.52 -> 12/12167}, {278.64 -> 10/12167}, {278.64 -> 2/12167}, {278.76 -> 12/12167}, {278.88 -> 6/12167}, {279.12 -> 3/12167}, {279.36 -> 13/12167}, {279.48 -> 15/12167}, {279.6 -> 12/12167}, {279.84 -> 12/12167}, {279.96 -> 4/12167}, {279.96 -> 2/12167}, {280.32 -> 2/12167}, {280.32 -> 4/12167}, {280.56 -> 3/12167}, {280.68 -> 18/12167}, {280.8 -> 6/12167}, {280.8 -> 18/12167}, {280.92 -> 12/12167}, {281.04 -> 6/12167}, {281.4 -> 3/12167}, {281.52 -> 4/12167}, {281.52 -> 2/12167}, {281.64 -> 9/12167}, {282.12 -> 6/12167}, {282.24 -> 12/12167}, {282.36 -> 12/12167}, {282.72 -> 2/12167}, {282.72 -> 4/12167}, {283.08 -> 2/12167}, {283.08 -> 10/12167}, {283.32 -> 6/12167}, {283.56 -> 12/12167}, {283.8 -> 6/12167}, {284.16 -> 4/12167}, {284.16 -> 8/12167}, {284.4 -> 12/12167}, {284.52 -> 3/12167}, {284.76 -> 3/12167}, {284.88 -> 15/12167}, {285.0 -> 15/12167}, {285.12 -> 6/12167}, {285.6 -> 6/12167}, {285.72 -> 2/12167}, {285.72 -> 10/12167}, {285.84 -> 2/12167}, {285.84 -> 4/12167}, {286.44 -> 6/12167}, {286.8 -> 6/12167}, {287.16 -> 2/12167}, {287.16 -> 4/12167}, {287.28 -> 6/12167}, {287.64 -> 8/12167}, {287.64 -> 4/12167}, {287.88 -> 18/12167}, {288.0 -> 6/12167}, {288.6 -> 12/12167}, {288.72 -> 6/12167}, {288.84 -> 9/12167}, {288.96 -> 8/12167}, {288.96 -> 4/12167}, {289.08 -> 3/12167}, {289.32 -> 4/12167}, {289.32 -> 2/12167}, {289.44 -> 6/12167}, {289.68 -> 18/12167}, {289.8 -> 4/12167}, {289.8 -> 8/12167}, {289.92 -> 12/12167}, {290.04 -> 6/12167}, {290.4 -> 3/12167}, {290.52 -> 14/12167}, {290.52 -> 4/12167}, {290.76 -> 6/12167}, {291.36 -> 3/12167}, {292.08 -> 3/12167}, {293.04 -> 2/12167}, {293.04 -> 4/12167}, {293.16 -> 4/12167}, {293.16 -> 2/12167}, {293.88 -> 12/12167}, {294.0 -> 12/12167}, {294.12 -> 6/12167}, {294.24 -> 6/12167}, {294.36 -> 9/12167}, {294.48 -> 2/12167}, {294.48 -> 4/12167}, {295.08 -> 6/12167}, {295.2 -> 12/12167}, {295.32 -> 18/12167}, {295.44 -> 12/12167}, {295.56 -> 2/12167}, {295.56 -> 4/12167}, {295.8 -> 3/12167}, {295.92 -> 1/12167}, {296.16 -> 4/12167}, {296.16 -> 11/12167}, {296.28 -> 3/12167}, {296.4 -> 12/12167}, {296.76 -> 6/12167}, {296.88 -> 6/12167}, {297.12 -> 6/12167}, {297.36 -> 3/12167}, {297.48 -> 2/12167}, {297.48 -> 4/12167}, {297.6 -> 1/12167}, {297.6 -> 20/12167}, {297.84 -> 6/12167}, {297.96 -> 3/12167}, {298.08 -> 6/12167}, {298.2 -> 3/12167}, {299.04 -> 2/12167}, {299.04 -> 4/12167}, {299.52 -> 6/12167}, {299.64 -> 6/12167}, {300.84 -> 6/12167}, {300.96 -> 6/12167}, {300.96 -> 6/12167}, {301.44 -> 3/12167}, {301.56 -> 12/12167}, {301.68 -> 6/12167}, {301.68 -> 15/12167}, {301.8 -> 4/12167}, {301.8 -> 8/12167}, {301.92 -> 6/12167}, {302.04 -> 6/12167}, {302.4 -> 11/12167}, {302.4 -> 4/12167}, {302.52 -> 12/12167}, {302.64 -> 6/12167}, {302.76 -> 6/12167}, {303.12 -> 9/12167}, {303.36 -> 3/12167}, {304.08 -> 6/12167}, {304.32 -> 3/12167}, {304.44 -> 6/12167}, {304.56 -> 2/12167}, {304.56 -> 1/12167}, {304.8 -> 3/12167}, {305.04 -> 2/12167}, {305.04 -> 4/12167}, {305.16 -> 6/12167}, {305.28 -> 6/12167}, {306.0 -> 6/12167}, {307.44 -> 4/12167}, {307.44 -> 2/12167}, {307.68 -> 3/12167}, {307.8 -> 4/12167}, {307.8 -> 5/12167}, {307.92 -> 7/12167}, {307.92 -> 2/12167}, {308.04 -> 5/12167}, {308.04 -> 4/12167}, {308.16 -> 4/12167}, {308.16 -> 2/12167}, {308.64 -> 6/12167}, {308.88 -> 3/12167}, {309.0 -> 3/12167}, {309.36 -> 6/12167}, {309.48 -> 2/12167}, {309.48 -> 4/12167}, {309.6 -> 6/12167}, {309.84 -> 4/12167}, {309.84 -> 8/12167}, {309.96 -> 3/12167}, {310.08 -> 10/12167}, {310.08 -> 2/12167}, {310.2 -> 3/12167}, {310.32 -> 1/12167}, {310.32 -> 2/12167}, {310.68 -> 18/12167}, {310.8 -> 2/12167}, {310.8 -> 4/12167}, {310.92 -> 4/12167}, {310.92 -> 8/12167}, {311.16 -> 3/12167}, {311.4 -> 1/12167}, {311.4 -> 2/12167}, {311.52 -> 12/12167}, {311.64 -> 9/12167}, {312.12 -> 6/12167}, {312.24 -> 6/12167}, {313.08 -> 2/12167}, {313.08 -> 4/12167}, {313.56 -> 6/12167}, {314.16 -> 2/12167}, {314.16 -> 7/12167}, {314.28 -> 3/12167}, {315.0 -> 6/12167}, {315.36 -> 1/12167}, {316.08 -> 3/12167}, {316.8 -> 3/12167}, {317.16 -> 6/12167}, {317.28 -> 6/12167}, {317.52 -> 1/12167}, {317.64 -> 4/12167}, {317.64 -> 2/12167}, {317.88 -> 6/12167}, {318.0 -> 6/12167}, {318.36 -> 6/12167}, {318.48 -> 2/12167}, {318.48 -> 4/12167}, {319.2 -> 4/12167}, {319.2 -> 2/12167}, {319.32 -> 6/12167}, {319.68 -> 6/12167}, {319.8 -> 2/12167}, {319.8 -> 4/12167}, {320.04 -> 2/12167}, {320.04 -> 4/12167}, {320.52 -> 4/12167}, {320.52 -> 2/12167}, {320.64 -> 12/12167}, {320.76 -> 6/12167}, {321.36 -> 6/12167}, {322.08 -> 2/12167}, {322.08 -> 4/12167}, {323.64 -> 3/12167}, {323.76 -> 6/12167}, {323.88 -> 9/12167}, {324.0 -> 6/12167}, {324.12 -> 6/12167}, {324.48 -> 6/12167}, {324.6 -> 4/12167}, {324.6 -> 8/12167}, {324.72 -> 2/12167}, {324.72 -> 7/12167}, {324.84 -> 4/12167}, {324.84 -> 8/12167}, {324.96 -> 3/12167}, {325.2 -> 3/12167}, {325.32 -> 7/12167}, {325.32 -> 2/12167}, {326.16 -> 10/12167}, {326.16 -> 14/12167}, {326.28 -> 6/12167}, {326.4 -> 6/12167}, {326.88 -> 6/12167}, {327.0 -> 12/12167}, {327.6 -> 6/12167}, {327.72 -> 6/12167}, {330.24 -> 6/12167}, {330.36 -> 12/12167}, {330.48 -> 2/12167}, {330.48 -> 4/12167}, {331.08 -> 6/12167}, {331.2 -> 2/12167}, {331.2 -> 4/12167}, {331.68 -> 6/12167}, {331.8 -> 2/12167}, {331.8 -> 4/12167}, {332.4 -> 4/12167}, {332.4 -> 2/12167}, {332.52 -> 6/12167}, {332.64 -> 6/12167}, {333.36 -> 6/12167}, {334.08 -> 2/12167}, {334.08 -> 4/12167}, {334.32 -> 8/12167}, {334.32 -> 4/12167}, {334.44 -> 6/12167}, {334.8 -> 6/12167}, {335.16 -> 8/12167}, {335.16 -> 4/12167}, {335.4 -> 6/12167}, {338.16 -> 3/12167}, {338.28 -> 3/12167}, {338.88 -> 6/12167}, {339.0 -> 6/12167}, {339.6 -> 3/12167}, {339.72 -> 3/12167}, {339.84 -> 2/12167}, {339.84 -> 4/12167}, {339.96 -> 3/12167}, {340.08 -> 4/12167}, {340.08 -> 2/12167}, {340.2 -> 3/12167}, {340.68 -> 12/12167}, {340.92 -> 2/12167}, {340.92 -> 4/12167}, {341.64 -> 3/12167}, {342.84 -> 2/12167}, {342.84 -> 4/12167}, {342.96 -> 2/12167}, {342.96 -> 4/12167}, {343.44 -> 6/12167}, {343.56 -> 6/12167}, {346.32 -> 4/12167}, {346.32 -> 2/12167}, {346.92 -> 6/12167}, {347.04 -> 8/12167}, {347.04 -> 4/12167}, {347.16 -> 8/12167}, {347.16 -> 4/12167}, {347.4 -> 6/12167}, {347.88 -> 12/12167}, {348.12 -> 6/12167}, {348.96 -> 3/12167}, {349.08 -> 4/12167}, {349.08 -> 2/12167}, {349.2 -> 3/12167}, {349.8 -> 6/12167}, {349.92 -> 4/12167}, {349.92 -> 2/12167}, {350.64 -> 6/12167}, {353.16 -> 4/12167}, {353.16 -> 2/12167}, {353.28 -> 10/12167}, {353.28 -> 2/12167}, {353.4 -> 6/12167}, {354.48 -> 3/12167}, {354.6 -> 2/12167}, {354.6 -> 4/12167}, {354.72 -> 1/12167}, {354.72 -> 2/12167}, {355.44 -> 6/12167}, {355.56 -> 6/12167}, {356.16 -> 4/12167}, {356.16 -> 2/12167}, {356.88 -> 6/12167}, {357.0 -> 6/12167}, {359.64 -> 3/12167}, {360.96 -> 3/12167}, {361.08 -> 4/12167}, {361.08 -> 2/12167}, {361.2 -> 3/12167}, {361.68 -> 3/12167}, {361.8 -> 4/12167}, {361.8 -> 2/12167}, {361.92 -> 3/12167}, {362.64 -> 6/12167}, {363.36 -> 6/12167}, {364.68 -> 3/12167}, {365.16 -> 4/12167}, {365.16 -> 2/12167}, {369.12 -> 6/12167}, {369.24 -> 6/12167}, {369.96 -> 4/12167}, {369.96 -> 8/12167}, {370.08 -> 4/12167}, {370.08 -> 8/12167}, {370.2 -> 4/12167}, {370.2 -> 2/12167}, {370.32 -> 6/12167}, {370.68 -> 3/12167}, {371.64 -> 6/12167}, {372.36 -> 6/12167}, {375.72 -> 3/12167}, {377.16 -> 4/12167}, {377.16 -> 2/12167}, {377.88 -> 6/12167}, {379.8 -> 3/12167}, {383.64 -> 3/12167}, {383.76 -> 1/12167}, {383.88 -> 3/12167}, {384.0 -> 3/12167}, {384.12 -> 1/12167}, {384.36 -> 6/12167}, {385.08 -> 3/12167}, {385.44 -> 4/12167}, {385.44 -> 2/12167}, {385.56 -> 2/12167}, {385.56 -> 4/12167}, {388.32 -> 1/12167}, {388.32 -> 2/12167}, {388.92 -> 3/12167}, {392.4 -> 2/12167}, {392.4 -> 1/12167}, {394.44 -> 4/12167}, {394.44 -> 2/12167}, {394.56 -> 2/12167}, {394.56 -> 4/12167}, {395.28 -> 2/12167}, {395.28 -> 1/12167}, {398.64 -> 3/12167}, {398.76 -> 3/12167}, {399.96 -> 2/12167}, {399.96 -> 4/12167}, {400.08 -> 2/12167}, {400.08 -> 4/12167}, {400.92 -> 3/12167}, {402.36 -> 3/12167}, {406.44 -> 4/12167}, {406.44 -> 2/12167}, {406.56 -> 2/12167}, {406.56 -> 4/12167}, {407.16 -> 4/12167}, {407.16 -> 2/12167}, {407.28 -> 6/12167}, {414.6 -> 3/12167}, {415.44 -> 2/12167}, {415.44 -> 4/12167}, {415.68 -> 3/12167}, {429.24 -> 3/12167}, {429.36 -> 6/12167}, {429.48 -> 3/12167}, {430.92 -> 2/12167}, {430.92 -> 1/12167}, {439.92 -> 2/12167}, {439.92 -> 1/12167}, {445.44 -> 1/12167}, {445.44 -> 2/12167}, {451.92 -> 2/12167}, {451.92 -> 1/12167}, {452.64 -> 3/12167}, {474.72 -> 3/12167}, {474.84 -> 3/12167}, {520.2 -> 1/12167}
In [46]:
PlotDist(Sys3)
In [47]:
PlotDist(CDF(Sys3))
In [48]:
U12 = UniformRV(1,2)
In [49]:
Un2n1 = UniformRV(-2,-1)
In [50]:
U12 + U12
continuous pdf
for 2 <= x <= 3
---------------------------
⎛ x⎞
1.0⋅log⎝ℯ ⎠ - 2.0
---------------------------
for 3 <= x <= 4
---------------------------
⎛ x⎞
- - -1.0⋅log⎝ℯ ⎠ + 4.0
---------------------------
Out[50]:
None
In [51]:
Un2n1 + Un2n1
continuous pdf
for -4 <= x <= -3
---------------------------
⎛ x⎞
1.0⋅log⎝ℯ ⎠ + 4.0
---------------------------
for -3 <= x <= -2
---------------------------
⎛ -1.0⎞
⎜⎛ x⎞ ⎟
log⎝⎝ℯ ⎠ ⎠ - 2.0
---------------------------
Out[51]:
None
In [52]:
U12+Un2n1
continuous pdf
for -1 <= x <= 0
---------------------------
⎛ x⎞
1.0⋅log⎝ℯ ⎠ + 1.0
---------------------------
for 0 <= x <= 1
---------------------------
⎛ x⎞
- - -1.0⋅log⎝ℯ ⎠ + 1.0
---------------------------
Out[52]:
None
In [53]:
Un2n1+U12
continuous pdf
for -1 <= x <= 0
---------------------------
⎛ x⎞
1.0⋅log⎝ℯ ⎠ + 1.0
---------------------------
for 0 <= x <= 1
---------------------------
⎛ x⎞
- - -1.0⋅log⎝ℯ ⎠ + 1.0
---------------------------
Out[53]:
None
In [54]:
U12*U12
continuous pdf
for 1 <= x <= 2
---------------------------
1.0⋅log(x)
---------------------------
for 2 <= x <= 4
---------------------------
⎛ 2.0 -1.0⎞
log⎝2 ⋅x ⎠
---------------------------
Out[54]:
None
In [55]:
Un2n1 * Un2n1
continuous pdf
for 1 <= x <= 2
---------------------------
1.0⋅log(x)
---------------------------
for 2 <= x <= 4
---------------------------
-- -1.0⋅log(x) + 2.0⋅log(2)
---------------------------
Out[55]:
None
In [56]:
U12 * Un2n1
continuous pdf
for -4 <= x <= -2
---------------------------
0
---------------------------
for -2 <= x <= -1
---------------------------
0
---------------------------
Out[56]:
None
In [57]:
Un2n1 * U12
continuous pdf
for -4 <= x <= -2
---------------------------
-- -1.0⋅log(-x) + 2.0⋅log(2)
---------------------------
for -2 <= x <= -1
---------------------------
1.0⋅log(-x)
---------------------------
Out[57]:
None
In [ ]:
Content source: MthwRobinson/APPLPy
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