Exercise 01

Q1: distribution P(x,y)

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In [12]:

import numpy
import matplotlib
import math
%matplotlib inline
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
R = numpy.arange(-4,4+1e-9,0.1)
x,y = numpy.meshgrid(R,R)

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Define the probability function (discrete)

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In [11]:

z = sum(sum(math.e**(-0.5*(x**2+y**2))))
F = 1/z*math.e**(-0.5*(x**2+y**2))
fig = plt.figure(figsize=(10,6))
ax = plt.axes(projection='3d')
ax.scatter(X,Y,F,s=1,alpha=0.5)

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Out[11]:

<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x10c33a2e8>

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Q2: conditional distribution

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In [15]:

z = sum(sum(math.e**(-0.5*(x**2+y**2))))
F = 1/z*math.e**(-0.5*(x**2+y**2))
Fcon = F*((x**2+y**2)**0.5>=1)
Fcon1 = Fcon/Fcon.sum()
fig = plt.figure(figsize=(10,6))
ax = plt.axes(projection='3d')
ax.scatter(X,Y,Fcon1,s=1,alpha=0.5)

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Out[15]:

<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x105918b00>

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Q3: Marginal distribution

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