In [1]:
theta = 0.6
rv = sp.stats.bernoulli(theta)
rv


Out[1]:
<scipy.stats._distn_infrastructure.rv_frozen at 0x7f76e93057d0>

In [4]:
xx = [0,1]
plt.bar(xx, rv.pmf(xx), align="center")
plt.xlim(-1, 2)
plt.ylim(0, 1)
plt.xticks([0, 1], ["X=0", "X=1"])
plt.ylabel("P(x)")
plt.title("pmf of Bernoulli distribution")


Out[4]:
<matplotlib.text.Text at 0x7f76e8c1c750>

In [5]:
coin = rv.rvs(100)

In [6]:
coin


Out[6]:
array([1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1,
       1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0,
       0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1,
       1, 1, 0, 1, 1, 0, 1, 1])

In [14]:
countplt= sns.countplot(coin)
plt.show(countplt)



In [18]:
y = np.bincount(coin, minlength=2) / len(coin)
df = pd.DataFrame({"theoretic": rv.pmf(xx), "simulation" : y}).stack()
df = df.reset_index()
df.columns = ["value", "type", "ratio"]
df


Out[18]:
value type ratio
0 0 simulation 0.31
1 0 theoretic 0.40
2 1 simulation 0.69
3 1 theoretic 0.60

In [19]:
sns.barplot(x="value", y="ratio", hue = "type", data=df)
plt.show()



In [20]:
N = 10
theta = 0.6
rv = sp.stats.binom(N,theta)
rv


Out[20]:
<scipy.stats._distn_infrastructure.rv_frozen at 0x7f76e19dc390>

In [22]:
xx = np.arange(N + 1)
plt.bar(xx, rv.pmf(xx), align="center")
plt.ylabel("P(x)")
plt.title("pmf of binomial distribution")
plt.show()



In [23]:
np.random.seed(0)
x = rv.rvs(100)
x


Out[23]:
array([ 6,  5,  6,  6,  6,  5,  6,  4,  3,  6,  5,  6,  6,  4,  8,  8,  9,
        5,  5,  4,  3,  5,  6,  5,  8,  5,  8,  4,  6,  6,  7,  5,  6,  6,
        9,  6,  6,  6,  4,  5,  7,  6,  5,  8,  5,  5,  7,  8,  7,  7,  6,
        6,  2,  8,  7,  8,  5,  7,  6,  7,  8,  8,  5,  8,  7,  7,  5,  8,
        4,  8,  3,  6,  3,  6,  5,  9,  7,  8,  7,  8,  7,  6,  8,  5,  6,
        7,  6,  8,  6,  4,  7,  5,  8,  5,  7,  7,  6,  9,  5, 10])

In [24]:
sns.countplot(x)
plt.show()



In [25]:
y = np.bincount(x, minlength=N) / len(x)
df = pd.DataFrame({"theoretic": rv.pmf(xx), "simulation" : y}).stack()
df = df.reset_index()
df.columns = ["value", "type", "ratio"]
df.head()


Out[25]:
value type ratio
0 0 simulation 0.000000
1 0 theoretic 0.000105
2 1 simulation 0.000000
3 1 theoretic 0.001573
4 2 simulation 0.010000

In [26]:
sns.barplot(x="value", y="ratio", hue="type", data = df)
plt.show()



In [32]:
a = np.arange(11)
rv.pmf([1,2,3])


Out[32]:
array([ 0.00157286,  0.01061683,  0.04246733])

In [35]:
rv.pmf?

In [38]:
np.random.seed(0)
x = np.random.randn(100)
plt.figure(figsize=(7,7))
sp.stats.probplot(x,plot=plt)
plt.axis("equal")
plt.show()



In [40]:
np.random.seed(0)
x = np.random.rand(100)
plt.figure(figsize=(7,7))
sp.stats.probplot(x,plot=plt)
plt.ylim(-0.5,1.5)
plt.show()



In [48]:
xx = np.linspace(-2, 2, 100)
plt.figure(figsize=(6,9))
for i, N in enumerate([1,2,30]):
    X = np.random.rand(1000, N) - 0.5
    S = X.sum(axis=1) / np.sqrt(N)
    plt.subplot(3, 2, 2*i+1)
    sns.distplot(S, bins=10, kde=False, norm_hist=True)
    plt.xlim(-2,2)
    plt.yticks([])
    plt.subplot(3,2,2*i+2)
    sp.stats.probplot(S, plot=plt)
    
plt.tight_layout()
plt.show()



In [46]:



Out[46]:
array([[  5.48813504e-01],
       [  7.15189366e-01],
       [  6.02763376e-01],
       [  5.44883183e-01],
       [  4.23654799e-01],
       [  6.45894113e-01],
       [  4.37587211e-01],
       [  8.91773001e-01],
       [  9.63662761e-01],
       [  3.83441519e-01],
       [  7.91725038e-01],
       [  5.28894920e-01],
       [  5.68044561e-01],
       [  9.25596638e-01],
       [  7.10360582e-02],
       [  8.71292997e-02],
       [  2.02183974e-02],
       [  8.32619846e-01],
       [  7.78156751e-01],
       [  8.70012148e-01],
       [  9.78618342e-01],
       [  7.99158564e-01],
       [  4.61479362e-01],
       [  7.80529176e-01],
       [  1.18274426e-01],
       [  6.39921021e-01],
       [  1.43353287e-01],
       [  9.44668917e-01],
       [  5.21848322e-01],
       [  4.14661940e-01],
       [  2.64555612e-01],
       [  7.74233689e-01],
       [  4.56150332e-01],
       [  5.68433949e-01],
       [  1.87898004e-02],
       [  6.17635497e-01],
       [  6.12095723e-01],
       [  6.16933997e-01],
       [  9.43748079e-01],
       [  6.81820299e-01],
       [  3.59507901e-01],
       [  4.37031954e-01],
       [  6.97631196e-01],
       [  6.02254716e-02],
       [  6.66766715e-01],
       [  6.70637870e-01],
       [  2.10382561e-01],
       [  1.28926298e-01],
       [  3.15428351e-01],
       [  3.63710771e-01],
       [  5.70196770e-01],
       [  4.38601513e-01],
       [  9.88373838e-01],
       [  1.02044811e-01],
       [  2.08876756e-01],
       [  1.61309518e-01],
       [  6.53108325e-01],
       [  2.53291603e-01],
       [  4.66310773e-01],
       [  2.44425592e-01],
       [  1.58969584e-01],
       [  1.10375141e-01],
       [  6.56329589e-01],
       [  1.38182951e-01],
       [  1.96582362e-01],
       [  3.68725171e-01],
       [  8.20993230e-01],
       [  9.71012758e-02],
       [  8.37944907e-01],
       [  9.60984079e-02],
       [  9.76459465e-01],
       [  4.68651202e-01],
       [  9.76761088e-01],
       [  6.04845520e-01],
       [  7.39263579e-01],
       [  3.91877923e-02],
       [  2.82806963e-01],
       [  1.20196561e-01],
       [  2.96140198e-01],
       [  1.18727719e-01],
       [  3.17983179e-01],
       [  4.14262995e-01],
       [  6.41474963e-02],
       [  6.92472119e-01],
       [  5.66601454e-01],
       [  2.65389491e-01],
       [  5.23248053e-01],
       [  9.39405108e-02],
       [  5.75946496e-01],
       [  9.29296198e-01],
       [  3.18568952e-01],
       [  6.67410380e-01],
       [  1.31797862e-01],
       [  7.16327204e-01],
       [  2.89406093e-01],
       [  1.83191362e-01],
       [  5.86512935e-01],
       [  2.01075462e-02],
       [  8.28940029e-01],
       [  4.69547619e-03],
       [  6.77816537e-01],
       [  2.70007973e-01],
       [  7.35194022e-01],
       [  9.62188545e-01],
       [  2.48753144e-01],
       [  5.76157334e-01],
       [  5.92041931e-01],
       [  5.72251906e-01],
       [  2.23081633e-01],
       [  9.52749012e-01],
       [  4.47125379e-01],
       [  8.46408672e-01],
       [  6.99479275e-01],
       [  2.97436951e-01],
       [  8.13797820e-01],
       [  3.96505741e-01],
       [  8.81103197e-01],
       [  5.81272873e-01],
       [  8.81735362e-01],
       [  6.92531590e-01],
       [  7.25254280e-01],
       [  5.01324382e-01],
       [  9.56083635e-01],
       [  6.43990199e-01],
       [  4.23855049e-01],
       [  6.06393214e-01],
       [  1.91931983e-02],
       [  3.01574817e-01],
       [  6.60173537e-01],
       [  2.90077607e-01],
       [  6.18015429e-01],
       [  4.28768701e-01],
       [  1.35474064e-01],
       [  2.98282326e-01],
       [  5.69964911e-01],
       [  5.90872761e-01],
       [  5.74325249e-01],
       [  6.53200820e-01],
       [  6.52103270e-01],
       [  4.31418435e-01],
       [  8.96546596e-01],
       [  3.67561870e-01],
       [  4.35864925e-01],
       [  8.91923355e-01],
       [  8.06193989e-01],
       [  7.03888584e-01],
       [  1.00226887e-01],
       [  9.19482614e-01],
       [  7.14241300e-01],
       [  9.98847007e-01],
       [  1.49448305e-01],
       [  8.68126057e-01],
       [  1.62492935e-01],
       [  6.15559564e-01],
       [  1.23819983e-01],
       [  8.48008229e-01],
       [  8.07318959e-01],
       [  5.69100739e-01],
       [  4.07183297e-01],
       [  6.91669955e-02],
       [  6.97428773e-01],
       [  4.53542683e-01],
       [  7.22055599e-01],
       [  8.66382326e-01],
       [  9.75521505e-01],
       [  8.55803342e-01],
       [  1.17140842e-02],
       [  3.59978064e-01],
       [  7.29990562e-01],
       [  1.71629677e-01],
       [  5.21036606e-01],
       [  5.43379883e-02],
       [  1.99996525e-01],
       [  1.85217945e-02],
       [  7.93697703e-01],
       [  2.23924688e-01],
       [  3.45351681e-01],
       [  9.28081293e-01],
       [  7.04414402e-01],
       [  3.18389295e-02],
       [  1.64694156e-01],
       [  6.21478401e-01],
       [  5.77228589e-01],
       [  2.37892821e-01],
       [  9.34213998e-01],
       [  6.13965956e-01],
       [  5.35632803e-01],
       [  5.89909976e-01],
       [  7.30122030e-01],
       [  3.11944995e-01],
       [  3.98221062e-01],
       [  2.09843749e-01],
       [  1.86193006e-01],
       [  9.44372390e-01],
       [  7.39550795e-01],
       [  4.90458809e-01],
       [  2.27414628e-01],
       [  2.54356482e-01],
       [  5.80291603e-02],
       [  4.34416626e-01],
       [  3.11795882e-01],
       [  6.96343489e-01],
       [  3.77751839e-01],
       [  1.79603678e-01],
       [  2.46787284e-02],
       [  6.72496315e-02],
       [  6.79392773e-01],
       [  4.53696845e-01],
       [  5.36579211e-01],
       [  8.96671293e-01],
       [  9.90338947e-01],
       [  2.16896984e-01],
       [  6.63078203e-01],
       [  2.63322377e-01],
       [  2.06509995e-02],
       [  7.58378654e-01],
       [  3.20017151e-01],
       [  3.83463894e-01],
       [  5.88317114e-01],
       [  8.31048455e-01],
       [  6.28981844e-01],
       [  8.72650655e-01],
       [  2.73542035e-01],
       [  7.98046834e-01],
       [  1.85635944e-01],
       [  9.52791657e-01],
       [  6.87488276e-01],
       [  2.15507677e-01],
       [  9.47370590e-01],
       [  7.30855807e-01],
       [  2.53941643e-01],
       [  2.13311977e-01],
       [  5.18200714e-01],
       [  2.56627181e-02],
       [  2.07470075e-01],
       [  4.24685469e-01],
       [  3.74169980e-01],
       [  4.63575424e-01],
       [  2.77628706e-01],
       [  5.86784346e-01],
       [  8.63855606e-01],
       [  1.17531856e-01],
       [  5.17379107e-01],
       [  1.32068106e-01],
       [  7.16859681e-01],
       [  3.96059703e-01],
       [  5.65421312e-01],
       [  1.83279836e-01],
       [  1.44847759e-01],
       [  4.88056281e-01],
       [  3.55612738e-01],
       [  9.40431945e-01],
       [  7.65325254e-01],
       [  7.48663620e-01],
       [  9.03719740e-01],
       [  8.34224354e-02],
       [  5.52192470e-01],
       [  5.84476069e-01],
       [  9.61936379e-01],
       [  2.92147527e-01],
       [  2.40828780e-01],
       [  1.00293942e-01],
       [  1.64296296e-02],
       [  9.29529317e-01],
       [  6.69916547e-01],
       [  7.85152912e-01],
       [  2.81730106e-01],
       [  5.86410166e-01],
       [  6.39552661e-02],
       [  4.85627596e-01],
       [  9.77495140e-01],
       [  8.76505245e-01],
       [  3.38158952e-01],
       [  9.61570155e-01],
       [  2.31701626e-01],
       [  9.49318822e-01],
       [  9.41377705e-01],
       [  7.99202587e-01],
       [  6.30447937e-01],
       [  8.74287967e-01],
       [  2.93020285e-01],
       [  8.48943555e-01],
       [  6.17876692e-01],
       [  1.32368578e-02],
       [  3.47233518e-01],
       [  1.48140861e-01],
       [  9.81829390e-01],
       [  4.78370307e-01],
       [  4.97391365e-01],
       [  6.39472516e-01],
       [  3.68584606e-01],
       [  1.36900272e-01],
       [  8.22117733e-01],
       [  1.89847912e-01],
       [  5.11318983e-01],
       [  2.24317029e-01],
       [  9.78444845e-02],
       [  8.62191517e-01],
       [  9.72919489e-01],
       [  9.60834658e-01],
       [  9.06555499e-01],
       [  7.74047333e-01],
       [  3.33145152e-01],
       [  8.11013900e-02],
       [  4.07241171e-01],
       [  2.32234142e-01],
       [  1.32487635e-01],
       [  5.34271818e-02],
       [  7.25594364e-01],
       [  1.14274586e-02],
       [  7.70580749e-01],
       [  1.46946645e-01],
       [  7.95220826e-02],
       [  8.96030342e-02],
       [  6.72047807e-01],
       [  2.45367210e-01],
       [  4.20539467e-01],
       [  5.57368791e-01],
       [  8.60551174e-01],
       [  7.27044263e-01],
       [  2.70327905e-01],
       [  1.31482799e-01],
       [  5.53743204e-02],
       [  3.01598634e-01],
       [  2.62118149e-01],
       [  4.56140567e-01],
       [  6.83281336e-01],
       [  6.95625446e-01],
       [  2.83518847e-01],
       [  3.79926956e-01],
       [  1.81150962e-01],
       [  7.88545512e-01],
       [  5.68480764e-02],
       [  6.96997242e-01],
       [  7.78695396e-01],
       [  7.77407562e-01],
       [  2.59422564e-01],
       [  3.73813138e-01],
       [  5.87599635e-01],
       [  2.72821902e-01],
       [  3.70852799e-01],
       [  1.97054280e-01],
       [  4.59855884e-01],
       [  4.46123013e-02],
       [  7.99795885e-01],
       [  7.69564470e-02],
       [  5.18835149e-01],
       [  3.06810100e-01],
       [  5.77542949e-01],
       [  9.59433341e-01],
       [  6.45570244e-01],
       [  3.53624358e-02],
       [  4.30402440e-01],
       [  5.10016852e-01],
       [  5.36177495e-01],
       [  6.81392511e-01],
       [  2.77596098e-01],
       [  1.28860565e-01],
       [  3.92675677e-01],
       [  9.56405723e-01],
       [  1.87130892e-01],
       [  9.03983955e-01],
       [  5.43805950e-01],
       [  4.56911422e-01],
       [  8.82041410e-01],
       [  4.58603962e-01],
       [  7.24167637e-01],
       [  3.99025322e-01],
       [  9.04044393e-01],
       [  6.90025020e-01],
       [  6.99622054e-01],
       [  3.27720402e-01],
       [  7.56778643e-01],
       [  6.36061055e-01],
       [  2.40020273e-01],
       [  1.60538822e-01],
       [  7.96391475e-01],
       [  9.59166603e-01],
       [  4.58138827e-01],
       [  5.90984165e-01],
       [  8.57722644e-01],
       [  4.57223453e-01],
       [  9.51874477e-01],
       [  5.75751162e-01],
       [  8.20767121e-01],
       [  9.08843718e-01],
       [  8.15523819e-01],
       [  1.59414463e-01],
       [  6.28898439e-01],
       [  3.98434259e-01],
       [  6.27129520e-02],
       [  4.24032252e-01],
       [  2.58684067e-01],
       [  8.49038308e-01],
       [  3.33046265e-02],
       [  9.58982722e-01],
       [  3.55368848e-01],
       [  3.56706890e-01],
       [  1.63285027e-02],
       [  1.85232325e-01],
       [  4.01259501e-01],
       [  9.29291417e-01],
       [  9.96149302e-02],
       [  9.45301533e-01],
       [  8.69488531e-01],
       [  4.54162397e-01],
       [  3.26700882e-01],
       [  2.32744129e-01],
       [  6.14464706e-01],
       [  3.30745915e-02],
       [  1.56060644e-02],
       [  4.28795722e-01],
       [  6.80740740e-02],
       [  2.51940988e-01],
       [  2.21160915e-01],
       [  2.53191194e-01],
       [  1.31055231e-01],
       [  1.20362229e-02],
       [  1.15484297e-01],
       [  6.18480260e-01],
       [  9.74256213e-01],
       [  9.90345002e-01],
       [  4.09054095e-01],
       [  1.62954426e-01],
       [  6.38761757e-01],
       [  4.90305347e-01],
       [  9.89409777e-01],
       [  6.53042072e-02],
       [  7.83234438e-01],
       [  2.88398497e-01],
       [  2.41418620e-01],
       [  6.62504572e-01],
       [  2.46063185e-01],
       [  6.65859118e-01],
       [  5.17308517e-01],
       [  4.24088988e-01],
       [  5.54687809e-01],
       [  2.87051520e-01],
       [  7.06574706e-01],
       [  4.14856869e-01],
       [  3.60545560e-01],
       [  8.28656915e-01],
       [  9.24966912e-01],
       [  4.60073109e-02],
       [  2.32626993e-01],
       [  3.48519369e-01],
       [  8.14966479e-01],
       [  9.85491428e-01],
       [  9.68971705e-01],
       [  9.04948346e-01],
       [  2.96556265e-01],
       [  9.92011243e-01],
       [  2.49420041e-01],
       [  1.05906155e-01],
       [  9.50952611e-01],
       [  2.33420255e-01],
       [  6.89768265e-01],
       [  5.83563590e-02],
       [  7.30709099e-01],
       [  8.81720212e-01],
       [  2.72436895e-01],
       [  3.79056896e-01],
       [  3.74296183e-01],
       [  7.48788258e-01],
       [  2.37807243e-01],
       [  1.71853099e-01],
       [  4.49291649e-01],
       [  3.04468407e-01],
       [  8.39189122e-01],
       [  2.37741826e-01],
       [  5.02389457e-01],
       [  9.42583600e-01],
       [  6.33997698e-01],
       [  8.67289405e-01],
       [  9.40209689e-01],
       [  7.50764862e-01],
       [  6.99575060e-01],
       [  9.67965567e-01],
       [  9.94400790e-01],
       [  4.51821683e-01],
       [  7.08697782e-02],
       [  2.92794031e-01],
       [  1.52354706e-01],
       [  4.17486375e-01],
       [  1.31289328e-01],
       [  6.04117804e-01],
       [  3.82808059e-01],
       [  8.95385884e-01],
       [  9.67794672e-01],
       [  5.46884902e-01],
       [  2.74823570e-01],
       [  5.92230419e-01],
       [  8.96761158e-01],
       [  4.06733346e-01],
       [  5.52078277e-01],
       [  2.71652768e-01],
       [  4.55444149e-01],
       [  4.01713535e-01],
       [  2.48413465e-01],
       [  5.05866384e-01],
       [  3.10380826e-01],
       [  3.73034864e-01],
       [  5.24970442e-01],
       [  7.50595023e-01],
       [  3.33507466e-01],
       [  9.24158767e-01],
       [  8.62318547e-01],
       [  4.86902960e-02],
       [  2.53642524e-01],
       [  4.46135513e-01],
       [  1.04627889e-01],
       [  3.48475989e-01],
       [  7.40097526e-01],
       [  6.80514481e-01],
       [  6.22384429e-01],
       [  7.10528403e-01],
       [  2.04923687e-01],
       [  3.41698115e-01],
       [  6.76242482e-01],
       [  8.79234763e-01],
       [  5.43678054e-01],
       [  2.82699651e-01],
       [  3.02352580e-02],
       [  7.10336829e-01],
       [  7.88410351e-03],
       [  3.72679070e-01],
       [  5.30537215e-01],
       [  9.22111462e-01],
       [  8.94945450e-02],
       [  4.05942322e-01],
       [  2.43131997e-02],
       [  3.42610984e-01],
       [  6.22231059e-01],
       [  2.79067948e-01],
       [  2.09749950e-01],
       [  1.15703233e-01],
       [  5.77140244e-01],
       [  6.95270006e-01],
       [  6.71957141e-01],
       [  9.48861021e-01],
       [  2.70321389e-03],
       [  6.47196654e-01],
       [  6.00392237e-01],
       [  5.88739610e-01],
       [  9.62770320e-01],
       [  1.68716734e-02],
       [  6.96482431e-01],
       [  8.13678650e-01],
       [  5.09807197e-01],
       [  3.33964870e-01],
       [  7.90840163e-01],
       [  9.72429256e-02],
       [  4.42035638e-01],
       [  5.19952375e-01],
       [  6.93956411e-01],
       [  9.08857320e-02],
       [  2.27759502e-01],
       [  4.10301563e-01],
       [  6.23294673e-01],
       [  8.86960781e-01],
       [  6.18826168e-01],
       [  1.33461471e-01],
       [  9.80580133e-01],
       [  8.71785735e-01],
       [  5.02720761e-01],
       [  9.22347982e-01],
       [  5.41380794e-01],
       [  9.23306068e-01],
       [  8.29897369e-01],
       [  9.68286410e-01],
       [  9.19782811e-01],
       [  3.60338174e-02],
       [  1.74772004e-01],
       [  3.89134677e-01],
       [  9.52142697e-01],
       [  3.00028919e-01],
       [  1.60467644e-01],
       [  8.86304666e-01],
       [  4.46394415e-01],
       [  9.07875594e-01],
       [  1.60230466e-01],
       [  6.61117512e-01],
       [  4.40263753e-01],
       [  7.64867690e-02],
       [  6.96463145e-01],
       [  2.47398756e-01],
       [  3.96155226e-02],
       [  5.99442982e-02],
       [  6.10785371e-02],
       [  9.07732957e-01],
       [  7.39883918e-01],
       [  8.98062357e-01],
       [  6.72582311e-01],
       [  5.28939929e-01],
       [  3.04446364e-01],
       [  9.97962251e-01],
       [  3.62189059e-01],
       [  4.70648949e-01],
       [  3.78245175e-01],
       [  9.79526929e-01],
       [  1.74658385e-01],
       [  3.27988001e-01],
       [  6.80348666e-01],
       [  6.32076183e-02],
       [  6.07249374e-01],
       [  4.77646503e-01],
       [  2.83999977e-01],
       [  2.38413281e-01],
       [  5.14512743e-01],
       [  3.67927581e-01],
       [  4.56519891e-01],
       [  3.37477382e-01],
       [  9.70493694e-01],
       [  1.33439432e-01],
       [  9.68039532e-02],
       [  3.43391729e-01],
       [  5.91026901e-01],
       [  6.59176472e-01],
       [  3.97256747e-01],
       [  9.99277994e-01],
       [  3.51892996e-01],
       [  7.21406668e-01],
       [  6.37582695e-01],
       [  8.13053863e-01],
       [  9.76225663e-01],
       [  8.89793656e-01],
       [  7.64561974e-01],
       [  6.98248478e-01],
       [  3.35498170e-01],
       [  1.47685578e-01],
       [  6.26360031e-02],
       [  2.41901704e-01],
       [  4.32281481e-01],
       [  5.21996274e-01],
       [  7.73083554e-01],
       [  9.58740923e-01],
       [  1.17320480e-01],
       [  1.07004140e-01],
       [  5.89694723e-01],
       [  7.45398074e-01],
       [  8.48150380e-01],
       [  9.35832080e-01],
       [  9.83426242e-01],
       [  3.99801692e-01],
       [  3.80335184e-01],
       [  1.47808677e-01],
       [  6.84934439e-01],
       [  6.56761958e-01],
       [  8.62062596e-01],
       [  9.72579948e-02],
       [  4.97776908e-01],
       [  5.81081930e-01],
       [  2.41557040e-01],
       [  1.69025406e-01],
       [  8.59580836e-01],
       [  5.85349222e-02],
       [  4.70620904e-01],
       [  1.15834001e-01],
       [  4.57058761e-01],
       [  9.79962326e-01],
       [  4.23706353e-01],
       [  8.57124918e-01],
       [  1.17315564e-01],
       [  2.71252077e-01],
       [  4.03792741e-01],
       [  3.99812140e-01],
       [  6.71383479e-01],
       [  3.44718127e-01],
       [  7.13766868e-01],
       [  6.39186899e-01],
       [  3.99161145e-01],
       [  4.31760128e-01],
       [  6.14527700e-01],
       [  7.00421901e-02],
       [  8.22406738e-01],
       [  6.53421161e-01],
       [  7.26342464e-01],
       [  5.36923001e-01],
       [  1.10477111e-01],
       [  4.05035613e-01],
       [  4.05373583e-01],
       [  3.21042990e-01],
       [  2.99503249e-02],
       [  7.37254243e-01],
       [  1.09784458e-01],
       [  6.06308133e-01],
       [  7.03217496e-01],
       [  6.34786323e-01],
       [  9.59142252e-01],
       [  1.03298155e-01],
       [  8.67167159e-01],
       [  2.91902348e-02],
       [  5.34916855e-01],
       [  4.04243618e-01],
       [  5.24183860e-01],
       [  3.65099877e-01],
       [  1.90566915e-01],
       [  1.91228974e-02],
       [  5.18149814e-01],
       [  8.42776863e-01],
       [  3.73215956e-01],
       [  2.22863818e-01],
       [  8.05320035e-02],
       [  8.53109231e-02],
       [  2.21396446e-01],
       [  1.00014061e-01],
       [  2.65039698e-01],
       [  6.61494621e-02],
       [  6.56048672e-02],
       [  8.56276180e-01],
       [  1.62120261e-01],
       [  5.59682406e-01],
       [  7.73455544e-01],
       [  4.56409565e-01],
       [  1.53368878e-01],
       [  1.99596142e-01],
       [  4.32984206e-01],
       [  5.28234089e-01],
       [  3.49440292e-01],
       [  7.81479600e-01],
       [  7.51021649e-01],
       [  9.27211807e-01],
       [  2.89525490e-02],
       [  8.95691291e-01],
       [  3.92568788e-01],
       [  8.78372495e-01],
       [  6.90784776e-01],
       [  9.87348757e-01],
       [  7.59282452e-01],
       [  3.64544626e-01],
       [  5.01063173e-01],
       [  3.76389155e-01],
       [  3.64911836e-01],
       [  2.60904499e-01],
       [  4.95970295e-01],
       [  6.81739945e-01],
       [  2.77340271e-01],
       [  5.24379811e-01],
       [  1.17380294e-01],
       [  1.59845287e-01],
       [  4.68063547e-02],
       [  9.70731443e-01],
       [  3.86035151e-03],
       [  1.78579968e-01],
       [  6.12866753e-01],
       [  8.13695989e-02],
       [  8.81896503e-01],
       [  7.19620158e-01],
       [  9.66389971e-01],
       [  5.07635547e-01],
       [  3.00403683e-01],
       [  5.49500573e-01],
       [  9.30818717e-01],
       [  5.20761437e-01],
       [  2.67207032e-01],
       [  8.77398789e-01],
       [  3.71918749e-01],
       [  1.38335000e-03],
       [  2.47685022e-01],
       [  3.18233509e-01],
       [  8.58777468e-01],
       [  4.58503167e-01],
       [  4.44587288e-01],
       [  3.36102266e-01],
       [  8.80678123e-01],
       [  9.45026777e-01],
       [  9.91890329e-01],
       [  3.76741267e-01],
       [  9.66147446e-01],
       [  7.91879570e-01],
       [  6.75689148e-01],
       [  2.44889479e-01],
       [  2.16457261e-01],
       [  1.66047825e-01],
       [  9.22756610e-01],
       [  2.94076662e-01],
       [  4.53094245e-01],
       [  4.93957834e-01],
       [  7.78171595e-01],
       [  8.44234962e-01],
       [  1.39072701e-01],
       [  4.26904360e-01],
       [  8.42854888e-01],
       [  8.18033306e-01],
       [  1.02413758e-01],
       [  1.56383349e-01],
       [  3.04198692e-01],
       [  7.53590691e-02],
       [  4.24663003e-01],
       [  1.07617705e-01],
       [  5.68217594e-01],
       [  2.46556940e-01],
       [  5.96433065e-01],
       [  1.17525643e-01],
       [  9.75883868e-01],
       [  9.32561204e-01],
       [  3.91796939e-01],
       [  2.42178594e-01],
       [  2.50398213e-01],
       [  4.83393535e-01],
       [  3.99928019e-02],
       [  6.39705106e-01],
       [  4.08302908e-01],
       [  3.77406573e-01],
       [  8.09364971e-01],
       [  7.09035460e-01],
       [  9.54333815e-01],
       [  3.51936240e-01],
       [  8.97542765e-01],
       [  7.69967186e-01],
       [  3.57424652e-01],
       [  6.21665436e-01],
       [  2.88569958e-01],
       [  8.74399917e-01],
       [  1.12427317e-01],
       [  2.12434361e-01],
       [  1.83033292e-01],
       [  4.03026002e-01],
       [  7.45232960e-01],
       [  5.26907449e-01],
       [  4.87676324e-01],
       [  5.45964897e-04],
       [  4.25401725e-01],
       [  6.35537748e-02],
       [  2.08253252e-01],
       [  9.32393939e-01],
       [  2.15398204e-01],
       [  8.58337639e-01],
       [  8.02893372e-01],
       [  1.59146237e-01],
       [  6.05711957e-01],
       [  1.15661872e-01],
       [  7.27888158e-01],
       [  6.37462277e-01],
       [  8.11938562e-01],
       [  4.79384549e-01],
       [  9.14863088e-01],
       [  4.93489468e-02],
       [  2.92888565e-01],
       [  7.15052597e-01],
       [  4.18109212e-01],
       [  1.72951354e-01],
       [  1.07210745e-01],
       [  8.17339111e-01],
       [  4.73142978e-01],
       [  8.82283672e-01],
       [  7.33289134e-01],
       [  4.09726206e-01],
       [  3.73511014e-01],
       [  5.15638347e-01],
       [  8.89059953e-01],
       [  7.37278580e-01],
       [  5.15296427e-03],
       [  6.94157851e-01],
       [  9.19507407e-01],
       [  7.10455760e-01],
       [  1.77005782e-01],
       [  4.83518127e-01],
       [  1.40316018e-01],
       [  3.58995278e-01],
       [  9.37117042e-01],
       [  9.23305308e-01],
       [  2.82836852e-01],
       [  3.39631044e-01],
       [  6.00212868e-01],
       [  9.63197295e-01],
       [  1.47801334e-01],
       [  2.56916644e-01],
       [  8.73556827e-01],
       [  4.91892232e-01],
       [  8.98961092e-01],
       [  1.85517898e-01],
       [  5.32668587e-01],
       [  3.26269633e-01],
       [  3.16542560e-01],
       [  4.46876964e-01],
       [  4.33077449e-01],
       [  3.57346880e-01],
       [  9.14970770e-01],
       [  7.31744185e-01],
       [  7.27546991e-01],
       [  2.89913450e-01],
       [  5.77709424e-01],
       [  7.79179433e-01],
       [  7.95590369e-01],
       [  3.44530461e-01],
       [  7.70872757e-01],
       [  7.35893897e-01],
       [  1.41506486e-01],
       [  8.65945469e-01],
       [  4.41321470e-01],
       [  4.86410449e-01],
       [  4.48369179e-01],
       [  5.67846001e-01],
       [  6.21169247e-01],
       [  4.98179566e-01],
       [  8.66788543e-01],
       [  6.27734756e-01],
       [  4.01427949e-01],
       [  4.16691757e-01],
       [  8.10838615e-01],
       [  3.48191943e-01],
       [  2.11454796e-01],
       [  5.93831880e-02],
       [  8.76026848e-01],
       [  9.18546451e-01],
       [  1.20120182e-01],
       [  3.34473741e-01],
       [  1.75372070e-01],
       [  1.15898469e-01],
       [  8.99866743e-01],
       [  5.68772591e-02],
       [  9.80485663e-01],
       [  9.64508607e-02],
       [  8.63470649e-01],
       [  5.66506107e-01],
       [  3.67917488e-01],
       [  3.42342377e-01],
       [  7.57364143e-01],
       [  3.14573295e-01],
       [  6.57318917e-01],
       [  5.17326084e-01],
       [  4.84965645e-01],
       [  9.01162171e-01],
       [  5.54645059e-01],
       [  8.26861603e-01],
       [  7.25573534e-01],
       [  3.85572461e-02],
       [  7.73110053e-01],
       [  2.16870250e-01],
       [  9.03149647e-01],
       [  4.29241906e-02],
       [  3.33072034e-01],
       [  9.97329472e-02],
       [  4.75589117e-01],
       [  8.20022436e-01],
       [  2.98187360e-01],
       [  1.50934897e-01],
       [  3.30267036e-01],
       [  8.13880142e-01],
       [  1.40383958e-01],
       [  2.27362449e-01],
       [  6.88519645e-02],
       [  7.05710044e-01],
       [  3.95233244e-01],
       [  3.10839977e-01],
       [  7.18626390e-01],
       [  3.35977542e-01],
       [  7.27771273e-01],
       [  8.15199395e-01],
       [  2.17662843e-01],
       [  9.73818697e-01],
       [  1.62357948e-01],
       [  2.90840907e-01],
       [  1.79795291e-01],
       [  3.45505656e-01],
       [  4.80060888e-01],
       [  5.22175869e-01],
       [  8.53606042e-01],
       [  8.89447909e-01],
       [  2.20103861e-01],
       [  6.22894032e-01],
       [  1.11496057e-01],
       [  4.58969860e-01],
       [  3.22333538e-01],
       [  3.16500745e-01],
       [  4.82584242e-01],
       [  7.29827636e-01],
       [  6.91826588e-02],
       [  8.79173338e-01],
       [  7.34813775e-01],
       [  1.76499389e-01],
       [  9.39160909e-01],
       [  5.06312224e-01],
       [  9.99808578e-01],
       [  1.97259474e-01],
       [  5.34908198e-01],
       [  2.90248043e-01],
       [  3.04173557e-01],
       [  5.91065381e-01],
       [  9.21719067e-01],
       [  8.05263856e-01],
       [  7.23941399e-01],
       [  5.59173782e-01],
       [  9.22298504e-01],
       [  4.92361407e-01],
       [  8.73832178e-01],
       [  8.33981644e-01],
       [  2.13835347e-01],
       [  7.71225463e-01],
       [  1.21711569e-02],
       [  3.22829538e-01],
       [  2.29567445e-01],
       [  5.06862958e-01],
       [  7.36853162e-01],
       [  9.76763674e-02],
       [  5.14922202e-01],
       [  9.38412022e-01],
       [  2.28646551e-01],
       [  6.77141144e-01]])

In [47]:
np.random.seed(0)
np.random.rand(1000,1) - 0.5


Out[47]:
array([[ 0.0488135 ],
       [ 0.21518937],
       [ 0.10276338],
       [ 0.04488318],
       [-0.0763452 ],
       [ 0.14589411],
       [-0.06241279],
       [ 0.391773  ],
       [ 0.46366276],
       [-0.11655848],
       [ 0.29172504],
       [ 0.02889492],
       [ 0.06804456],
       [ 0.42559664],
       [-0.42896394],
       [-0.4128707 ],
       [-0.4797816 ],
       [ 0.33261985],
       [ 0.27815675],
       [ 0.37001215],
       [ 0.47861834],
       [ 0.29915856],
       [-0.03852064],
       [ 0.28052918],
       [-0.38172557],
       [ 0.13992102],
       [-0.35664671],
       [ 0.44466892],
       [ 0.02184832],
       [-0.08533806],
       [-0.23544439],
       [ 0.27423369],
       [-0.04384967],
       [ 0.06843395],
       [-0.4812102 ],
       [ 0.1176355 ],
       [ 0.11209572],
       [ 0.116934  ],
       [ 0.44374808],
       [ 0.1818203 ],
       [-0.1404921 ],
       [-0.06296805],
       [ 0.1976312 ],
       [-0.43977453],
       [ 0.16676672],
       [ 0.17063787],
       [-0.28961744],
       [-0.3710737 ],
       [-0.18457165],
       [-0.13628923],
       [ 0.07019677],
       [-0.06139849],
       [ 0.48837384],
       [-0.39795519],
       [-0.29112324],
       [-0.33869048],
       [ 0.15310833],
       [-0.2467084 ],
       [-0.03368923],
       [-0.25557441],
       [-0.34103042],
       [-0.38962486],
       [ 0.15632959],
       [-0.36181705],
       [-0.30341764],
       [-0.13127483],
       [ 0.32099323],
       [-0.40289872],
       [ 0.33794491],
       [-0.40390159],
       [ 0.47645947],
       [-0.0313488 ],
       [ 0.47676109],
       [ 0.10484552],
       [ 0.23926358],
       [-0.46081221],
       [-0.21719304],
       [-0.37980344],
       [-0.2038598 ],
       [-0.38127228],
       [-0.18201682],
       [-0.08573701],
       [-0.4358525 ],
       [ 0.19247212],
       [ 0.06660145],
       [-0.23461051],
       [ 0.02324805],
       [-0.40605949],
       [ 0.0759465 ],
       [ 0.4292962 ],
       [-0.18143105],
       [ 0.16741038],
       [-0.36820214],
       [ 0.2163272 ],
       [-0.21059391],
       [-0.31680864],
       [ 0.08651293],
       [-0.47989245],
       [ 0.32894003],
       [-0.49530452],
       [ 0.17781654],
       [-0.22999203],
       [ 0.23519402],
       [ 0.46218855],
       [-0.25124686],
       [ 0.07615733],
       [ 0.09204193],
       [ 0.07225191],
       [-0.27691837],
       [ 0.45274901],
       [-0.05287462],
       [ 0.34640867],
       [ 0.19947928],
       [-0.20256305],
       [ 0.31379782],
       [-0.10349426],
       [ 0.3811032 ],
       [ 0.08127287],
       [ 0.38173536],
       [ 0.19253159],
       [ 0.22525428],
       [ 0.00132438],
       [ 0.45608363],
       [ 0.1439902 ],
       [-0.07614495],
       [ 0.10639321],
       [-0.4808068 ],
       [-0.19842518],
       [ 0.16017354],
       [-0.20992239],
       [ 0.11801543],
       [-0.0712313 ],
       [-0.36452594],
       [-0.20171767],
       [ 0.06996491],
       [ 0.09087276],
       [ 0.07432525],
       [ 0.15320082],
       [ 0.15210327],
       [-0.06858156],
       [ 0.3965466 ],
       [-0.13243813],
       [-0.06413507],
       [ 0.39192336],
       [ 0.30619399],
       [ 0.20388858],
       [-0.39977311],
       [ 0.41948261],
       [ 0.2142413 ],
       [ 0.49884701],
       [-0.3505517 ],
       [ 0.36812606],
       [-0.33750707],
       [ 0.11555956],
       [-0.37618002],
       [ 0.34800823],
       [ 0.30731896],
       [ 0.06910074],
       [-0.0928167 ],
       [-0.430833  ],
       [ 0.19742877],
       [-0.04645732],
       [ 0.2220556 ],
       [ 0.36638233],
       [ 0.47552151],
       [ 0.35580334],
       [-0.48828592],
       [-0.14002194],
       [ 0.22999056],
       [-0.32837032],
       [ 0.02103661],
       [-0.44566201],
       [-0.30000348],
       [-0.48147821],
       [ 0.2936977 ],
       [-0.27607531],
       [-0.15464832],
       [ 0.42808129],
       [ 0.2044144 ],
       [-0.46816107],
       [-0.33530584],
       [ 0.1214784 ],
       [ 0.07722859],
       [-0.26210718],
       [ 0.434214  ],
       [ 0.11396596],
       [ 0.0356328 ],
       [ 0.08990998],
       [ 0.23012203],
       [-0.188055  ],
       [-0.10177894],
       [-0.29015625],
       [-0.31380699],
       [ 0.44437239],
       [ 0.2395508 ],
       [-0.00954119],
       [-0.27258537],
       [-0.24564352],
       [-0.44197084],
       [-0.06558337],
       [-0.18820412],
       [ 0.19634349],
       [-0.12224816],
       [-0.32039632],
       [-0.47532127],
       [-0.43275037],
       [ 0.17939277],
       [-0.04630316],
       [ 0.03657921],
       [ 0.39667129],
       [ 0.49033895],
       [-0.28310302],
       [ 0.1630782 ],
       [-0.23667762],
       [-0.479349  ],
       [ 0.25837865],
       [-0.17998285],
       [-0.11653611],
       [ 0.08831711],
       [ 0.33104846],
       [ 0.12898184],
       [ 0.37265066],
       [-0.22645797],
       [ 0.29804683],
       [-0.31436406],
       [ 0.45279166],
       [ 0.18748828],
       [-0.28449232],
       [ 0.44737059],
       [ 0.23085581],
       [-0.24605836],
       [-0.28668802],
       [ 0.01820071],
       [-0.47433728],
       [-0.29252992],
       [-0.07531453],
       [-0.12583002],
       [-0.03642458],
       [-0.22237129],
       [ 0.08678435],
       [ 0.36385561],
       [-0.38246814],
       [ 0.01737911],
       [-0.36793189],
       [ 0.21685968],
       [-0.1039403 ],
       [ 0.06542131],
       [-0.31672016],
       [-0.35515224],
       [-0.01194372],
       [-0.14438726],
       [ 0.44043195],
       [ 0.26532525],
       [ 0.24866362],
       [ 0.40371974],
       [-0.41657756],
       [ 0.05219247],
       [ 0.08447607],
       [ 0.46193638],
       [-0.20785247],
       [-0.25917122],
       [-0.39970606],
       [-0.48357037],
       [ 0.42952932],
       [ 0.16991655],
       [ 0.28515291],
       [-0.21826989],
       [ 0.08641017],
       [-0.43604473],
       [-0.0143724 ],
       [ 0.47749514],
       [ 0.37650525],
       [-0.16184105],
       [ 0.46157015],
       [-0.26829837],
       [ 0.44931882],
       [ 0.4413777 ],
       [ 0.29920259],
       [ 0.13044794],
       [ 0.37428797],
       [-0.20697972],
       [ 0.34894356],
       [ 0.11787669],
       [-0.48676314],
       [-0.15276648],
       [-0.35185914],
       [ 0.48182939],
       [-0.02162969],
       [-0.00260863],
       [ 0.13947252],
       [-0.13141539],
       [-0.36309973],
       [ 0.32211773],
       [-0.31015209],
       [ 0.01131898],
       [-0.27568297],
       [-0.40215552],
       [ 0.36219152],
       [ 0.47291949],
       [ 0.46083466],
       [ 0.4065555 ],
       [ 0.27404733],
       [-0.16685485],
       [-0.41889861],
       [-0.09275883],
       [-0.26776586],
       [-0.36751237],
       [-0.44657282],
       [ 0.22559436],
       [-0.48857254],
       [ 0.27058075],
       [-0.35305335],
       [-0.42047792],
       [-0.41039697],
       [ 0.17204781],
       [-0.25463279],
       [-0.07946053],
       [ 0.05736879],
       [ 0.36055117],
       [ 0.22704426],
       [-0.22967209],
       [-0.3685172 ],
       [-0.44462568],
       [-0.19840137],
       [-0.23788185],
       [-0.04385943],
       [ 0.18328134],
       [ 0.19562545],
       [-0.21648115],
       [-0.12007304],
       [-0.31884904],
       [ 0.28854551],
       [-0.44315192],
       [ 0.19699724],
       [ 0.2786954 ],
       [ 0.27740756],
       [-0.24057744],
       [-0.12618686],
       [ 0.08759964],
       [-0.2271781 ],
       [-0.1291472 ],
       [-0.30294572],
       [-0.04014412],
       [-0.4553877 ],
       [ 0.29979588],
       [-0.42304355],
       [ 0.01883515],
       [-0.1931899 ],
       [ 0.07754295],
       [ 0.45943334],
       [ 0.14557024],
       [-0.46463756],
       [-0.06959756],
       [ 0.01001685],
       [ 0.03617749],
       [ 0.18139251],
       [-0.2224039 ],
       [-0.37113943],
       [-0.10732432],
       [ 0.45640572],
       [-0.31286911],
       [ 0.40398395],
       [ 0.04380595],
       [-0.04308858],
       [ 0.38204141],
       [-0.04139604],
       [ 0.22416764],
       [-0.10097468],
       [ 0.40404439],
       [ 0.19002502],
       [ 0.19962205],
       [-0.1722796 ],
       [ 0.25677864],
       [ 0.13606106],
       [-0.25997973],
       [-0.33946118],
       [ 0.29639147],
       [ 0.4591666 ],
       [-0.04186117],
       [ 0.09098417],
       [ 0.35772264],
       [-0.04277655],
       [ 0.45187448],
       [ 0.07575116],
       [ 0.32076712],
       [ 0.40884372],
       [ 0.31552382],
       [-0.34058554],
       [ 0.12889844],
       [-0.10156574],
       [-0.43728705],
       [-0.07596775],
       [-0.24131593],
       [ 0.34903831],
       [-0.46669537],
       [ 0.45898272],
       [-0.14463115],
       [-0.14329311],
       [-0.4836715 ],
       [-0.31476767],
       [-0.0987405 ],
       [ 0.42929142],
       [-0.40038507],
       [ 0.44530153],
       [ 0.36948853],
       [-0.0458376 ],
       [-0.17329912],
       [-0.26725587],
       [ 0.11446471],
       [-0.46692541],
       [-0.48439394],
       [-0.07120428],
       [-0.43192593],
       [-0.24805901],
       [-0.27883908],
       [-0.24680881],
       [-0.36894477],
       [-0.48796378],
       [-0.3845157 ],
       [ 0.11848026],
       [ 0.47425621],
       [ 0.490345  ],
       [-0.0909459 ],
       [-0.33704557],
       [ 0.13876176],
       [-0.00969465],
       [ 0.48940978],
       [-0.43469579],
       [ 0.28323444],
       [-0.2116015 ],
       [-0.25858138],
       [ 0.16250457],
       [-0.25393682],
       [ 0.16585912],
       [ 0.01730852],
       [-0.07591101],
       [ 0.05468781],
       [-0.21294848],
       [ 0.20657471],
       [-0.08514313],
       [-0.13945444],
       [ 0.32865691],
       [ 0.42496691],
       [-0.45399269],
       [-0.26737301],
       [-0.15148063],
       [ 0.31496648],
       [ 0.48549143],
       [ 0.4689717 ],
       [ 0.40494835],
       [-0.20344373],
       [ 0.49201124],
       [-0.25057996],
       [-0.39409385],
       [ 0.45095261],
       [-0.26657974],
       [ 0.18976827],
       [-0.44164364],
       [ 0.2307091 ],
       [ 0.38172021],
       [-0.2275631 ],
       [-0.1209431 ],
       [-0.12570382],
       [ 0.24878826],
       [-0.26219276],
       [-0.3281469 ],
       [-0.05070835],
       [-0.19553159],
       [ 0.33918912],
       [-0.26225817],
       [ 0.00238946],
       [ 0.4425836 ],
       [ 0.1339977 ],
       [ 0.36728941],
       [ 0.44020969],
       [ 0.25076486],
       [ 0.19957506],
       [ 0.46796557],
       [ 0.49440079],
       [-0.04817832],
       [-0.42913022],
       [-0.20720597],
       [-0.34764529],
       [-0.08251363],
       [-0.36871067],
       [ 0.1041178 ],
       [-0.11719194],
       [ 0.39538588],
       [ 0.46779467],
       [ 0.0468849 ],
       [-0.22517643],
       [ 0.09223042],
       [ 0.39676116],
       [-0.09326665],
       [ 0.05207828],
       [-0.22834723],
       [-0.04455585],
       [-0.09828646],
       [-0.25158653],
       [ 0.00586638],
       [-0.18961917],
       [-0.12696514],
       [ 0.02497044],
       [ 0.25059502],
       [-0.16649253],
       [ 0.42415877],
       [ 0.36231855],
       [-0.4513097 ],
       [-0.24635748],
       [-0.05386449],
       [-0.39537211],
       [-0.15152401],
       [ 0.24009753],
       [ 0.18051448],
       [ 0.12238443],
       [ 0.2105284 ],
       [-0.29507631],
       [-0.15830189],
       [ 0.17624248],
       [ 0.37923476],
       [ 0.04367805],
       [-0.21730035],
       [-0.46976474],
       [ 0.21033683],
       [-0.4921159 ],
       [-0.12732093],
       [ 0.03053721],
       [ 0.42211146],
       [-0.41050545],
       [-0.09405768],
       [-0.4756868 ],
       [-0.15738902],
       [ 0.12223106],
       [-0.22093205],
       [-0.29025005],
       [-0.38429677],
       [ 0.07714024],
       [ 0.19527001],
       [ 0.17195714],
       [ 0.44886102],
       [-0.49729679],
       [ 0.14719665],
       [ 0.10039224],
       [ 0.08873961],
       [ 0.46277032],
       [-0.48312833],
       [ 0.19648243],
       [ 0.31367865],
       [ 0.0098072 ],
       [-0.16603513],
       [ 0.29084016],
       [-0.40275707],
       [-0.05796436],
       [ 0.01995237],
       [ 0.19395641],
       [-0.40911427],
       [-0.2722405 ],
       [-0.08969844],
       [ 0.12329467],
       [ 0.38696078],
       [ 0.11882617],
       [-0.36653853],
       [ 0.48058013],
       [ 0.37178573],
       [ 0.00272076],
       [ 0.42234798],
       [ 0.04138079],
       [ 0.42330607],
       [ 0.32989737],
       [ 0.46828641],
       [ 0.41978281],
       [-0.46396618],
       [-0.325228  ],
       [-0.11086532],
       [ 0.4521427 ],
       [-0.19997108],
       [-0.33953236],
       [ 0.38630467],
       [-0.05360558],
       [ 0.40787559],
       [-0.33976953],
       [ 0.16111751],
       [-0.05973625],
       [-0.42351323],
       [ 0.19646314],
       [-0.25260124],
       [-0.46038448],
       [-0.4400557 ],
       [-0.43892146],
       [ 0.40773296],
       [ 0.23988392],
       [ 0.39806236],
       [ 0.17258231],
       [ 0.02893993],
       [-0.19555364],
       [ 0.49796225],
       [-0.13781094],
       [-0.02935105],
       [-0.12175483],
       [ 0.47952693],
       [-0.32534161],
       [-0.172012  ],
       [ 0.18034867],
       [-0.43679238],
       [ 0.10724937],
       [-0.0223535 ],
       [-0.21600002],
       [-0.26158672],
       [ 0.01451274],
       [-0.13207242],
       [-0.04348011],
       [-0.16252262],
       [ 0.47049369],
       [-0.36656057],
       [-0.40319605],
       [-0.15660827],
       [ 0.0910269 ],
       [ 0.15917647],
       [-0.10274325],
       [ 0.49927799],
       [-0.148107  ],
       [ 0.22140667],
       [ 0.13758269],
       [ 0.31305386],
       [ 0.47622566],
       [ 0.38979366],
       [ 0.26456197],
       [ 0.19824848],
       [-0.16450183],
       [-0.35231442],
       [-0.437364  ],
       [-0.2580983 ],
       [-0.06771852],
       [ 0.02199627],
       [ 0.27308355],
       [ 0.45874092],
       [-0.38267952],
       [-0.39299586],
       [ 0.08969472],
       [ 0.24539807],
       [ 0.34815038],
       [ 0.43583208],
       [ 0.48342624],
       [-0.10019831],
       [-0.11966482],
       [-0.35219132],
       [ 0.18493444],
       [ 0.15676196],
       [ 0.3620626 ],
       [-0.40274201],
       [-0.00222309],
       [ 0.08108193],
       [-0.25844296],
       [-0.33097459],
       [ 0.35958084],
       [-0.44146508],
       [-0.0293791 ],
       [-0.384166  ],
       [-0.04294124],
       [ 0.47996233],
       [-0.07629365],
       [ 0.35712492],
       [-0.38268444],
       [-0.22874792],
       [-0.09620726],
       [-0.10018786],
       [ 0.17138348],
       [-0.15528187],
       [ 0.21376687],
       [ 0.1391869 ],
       [-0.10083885],
       [-0.06823987],
       [ 0.1145277 ],
       [-0.42995781],
       [ 0.32240674],
       [ 0.15342116],
       [ 0.22634246],
       [ 0.036923  ],
       [-0.38952289],
       [-0.09496439],
       [-0.09462642],
       [-0.17895701],
       [-0.47004968],
       [ 0.23725424],
       [-0.39021554],
       [ 0.10630813],
       [ 0.2032175 ],
       [ 0.13478632],
       [ 0.45914225],
       [-0.39670184],
       [ 0.36716716],
       [-0.47080977],
       [ 0.03491685],
       [-0.09575638],
       [ 0.02418386],
       [-0.13490012],
       [-0.30943309],
       [-0.4808771 ],
       [ 0.01814981],
       [ 0.34277686],
       [-0.12678404],
       [-0.27713618],
       [-0.419468  ],
       [-0.41468908],
       [-0.27860355],
       [-0.39998594],
       [-0.2349603 ],
       [-0.43385054],
       [-0.43439513],
       [ 0.35627618],
       [-0.33787974],
       [ 0.05968241],
       [ 0.27345554],
       [-0.04359043],
       [-0.34663112],
       [-0.30040386],
       [-0.06701579],
       [ 0.02823409],
       [-0.15055971],
       [ 0.2814796 ],
       [ 0.25102165],
       [ 0.42721181],
       [-0.47104745],
       [ 0.39569129],
       [-0.10743121],
       [ 0.3783725 ],
       [ 0.19078478],
       [ 0.48734876],
       [ 0.25928245],
       [-0.13545537],
       [ 0.00106317],
       [-0.12361084],
       [-0.13508816],
       [-0.2390955 ],
       [-0.0040297 ],
       [ 0.18173995],
       [-0.22265973],
       [ 0.02437981],
       [-0.38261971],
       [-0.34015471],
       [-0.45319365],
       [ 0.47073144],
       [-0.49613965],
       [-0.32142003],
       [ 0.11286675],
       [-0.4186304 ],
       [ 0.3818965 ],
       [ 0.21962016],
       [ 0.46638997],
       [ 0.00763555],
       [-0.19959632],
       [ 0.04950057],
       [ 0.43081872],
       [ 0.02076144],
       [-0.23279297],
       [ 0.37739879],
       [-0.12808125],
       [-0.49861665],
       [-0.25231498],
       [-0.18176649],
       [ 0.35877747],
       [-0.04149683],
       [-0.05541271],
       [-0.16389773],
       [ 0.38067812],
       [ 0.44502678],
       [ 0.49189033],
       [-0.12325873],
       [ 0.46614745],
       [ 0.29187957],
       [ 0.17568915],
       [-0.25511052],
       [-0.28354274],
       [-0.33395218],
       [ 0.42275661],
       [-0.20592334],
       [-0.04690575],
       [-0.00604217],
       [ 0.2781716 ],
       [ 0.34423496],
       [-0.3609273 ],
       [-0.07309564],
       [ 0.34285489],
       [ 0.31803331],
       [-0.39758624],
       [-0.34361665],
       [-0.19580131],
       [-0.42464093],
       [-0.075337  ],
       [-0.39238229],
       [ 0.06821759],
       [-0.25344306],
       [ 0.09643307],
       [-0.38247436],
       [ 0.47588387],
       [ 0.4325612 ],
       [-0.10820306],
       [-0.25782141],
       [-0.24960179],
       [-0.01660646],
       [-0.4600072 ],
       [ 0.13970511],
       [-0.09169709],
       [-0.12259343],
       [ 0.30936497],
       [ 0.20903546],
       [ 0.45433382],
       [-0.14806376],
       [ 0.39754276],
       [ 0.26996719],
       [-0.14257535],
       [ 0.12166544],
       [-0.21143004],
       [ 0.37439992],
       [-0.38757268],
       [-0.28756564],
       [-0.31696671],
       [-0.096974  ],
       [ 0.24523296],
       [ 0.02690745],
       [-0.01232368],
       [-0.49945404],
       [-0.07459827],
       [-0.43644623],
       [-0.29174675],
       [ 0.43239394],
       [-0.2846018 ],
       [ 0.35833764],
       [ 0.30289337],
       [-0.34085376],
       [ 0.10571196],
       [-0.38433813],
       [ 0.22788816],
       [ 0.13746228],
       [ 0.31193856],
       [-0.02061545],
       [ 0.41486309],
       [-0.45065105],
       [-0.20711143],
       [ 0.2150526 ],
       [-0.08189079],
       [-0.32704865],
       [-0.39278925],
       [ 0.31733911],
       [-0.02685702],
       [ 0.38228367],
       [ 0.23328913],
       [-0.09027379],
       [-0.12648899],
       [ 0.01563835],
       [ 0.38905995],
       [ 0.23727858],
       [-0.49484704],
       [ 0.19415785],
       [ 0.41950741],
       [ 0.21045576],
       [-0.32299422],
       [-0.01648187],
       [-0.35968398],
       [-0.14100472],
       [ 0.43711704],
       [ 0.42330531],
       [-0.21716315],
       [-0.16036896],
       [ 0.10021287],
       [ 0.4631973 ],
       [-0.35219867],
       [-0.24308336],
       [ 0.37355683],
       [-0.00810777],
       [ 0.39896109],
       [-0.3144821 ],
       [ 0.03266859],
       [-0.17373037],
       [-0.18345744],
       [-0.05312304],
       [-0.06692255],
       [-0.14265312],
       [ 0.41497077],
       [ 0.23174419],
       [ 0.22754699],
       [-0.21008655],
       [ 0.07770942],
       [ 0.27917943],
       [ 0.29559037],
       [-0.15546954],
       [ 0.27087276],
       [ 0.2358939 ],
       [-0.35849351],
       [ 0.36594547],
       [-0.05867853],
       [-0.01358955],
       [-0.05163082],
       [ 0.067846  ],
       [ 0.12116925],
       [-0.00182043],
       [ 0.36678854],
       [ 0.12773476],
       [-0.09857205],
       [-0.08330824],
       [ 0.31083862],
       [-0.15180806],
       [-0.2885452 ],
       [-0.44061681],
       [ 0.37602685],
       [ 0.41854645],
       [-0.37987982],
       [-0.16552626],
       [-0.32462793],
       [-0.38410153],
       [ 0.39986674],
       [-0.44312274],
       [ 0.48048566],
       [-0.40354914],
       [ 0.36347065],
       [ 0.06650611],
       [-0.13208251],
       [-0.15765762],
       [ 0.25736414],
       [-0.1854267 ],
       [ 0.15731892],
       [ 0.01732608],
       [-0.01503435],
       [ 0.40116217],
       [ 0.05464506],
       [ 0.3268616 ],
       [ 0.22557353],
       [-0.46144275],
       [ 0.27311005],
       [-0.28312975],
       [ 0.40314965],
       [-0.45707581],
       [-0.16692797],
       [-0.40026705],
       [-0.02441088],
       [ 0.32002244],
       [-0.20181264],
       [-0.3490651 ],
       [-0.16973296],
       [ 0.31388014],
       [-0.35961604],
       [-0.27263755],
       [-0.43114804],
       [ 0.20571004],
       [-0.10476676],
       [-0.18916002],
       [ 0.21862639],
       [-0.16402246],
       [ 0.22777127],
       [ 0.3151994 ],
       [-0.28233716],
       [ 0.4738187 ],
       [-0.33764205],
       [-0.20915909],
       [-0.32020471],
       [-0.15449434],
       [-0.01993911],
       [ 0.02217587],
       [ 0.35360604],
       [ 0.38944791],
       [-0.27989614],
       [ 0.12289403],
       [-0.38850394],
       [-0.04103014],
       [-0.17766646],
       [-0.18349925],
       [-0.01741576],
       [ 0.22982764],
       [-0.43081734],
       [ 0.37917334],
       [ 0.23481377],
       [-0.32350061],
       [ 0.43916091],
       [ 0.00631222],
       [ 0.49980858],
       [-0.30274053],
       [ 0.0349082 ],
       [-0.20975196],
       [-0.19582644],
       [ 0.09106538],
       [ 0.42171907],
       [ 0.30526386],
       [ 0.2239414 ],
       [ 0.05917378],
       [ 0.4222985 ],
       [-0.00763859],
       [ 0.37383218],
       [ 0.33398164],
       [-0.28616465],
       [ 0.27122546],
       [-0.48782884],
       [-0.17717046],
       [-0.27043256],
       [ 0.00686296],
       [ 0.23685316],
       [-0.40232363],
       [ 0.0149222 ],
       [ 0.43841202],
       [-0.27135345],
       [ 0.17714114]])

In [ ]: