>>> s = sp.randn(100)
>>> s
array([ 0.81846905, -0.206404 , 0.04115042, 0.51684893, 0.16637882,
-0.73836188, -0.08306182, -0.58723059, -0.24179899, 1.04275659,
0.24947425, -0.82042454, -1.7403959 , 0.19852693, -0.29634134,
0.46413926, 0.99778752, -1.1042843 , 0.68394051, 0.61526696,
0.87677284, 0.4744107 , 0.49778494, -0.37790903, -0.41810024,
-0.92315847, -0.29561186, 1.05319456, -0.82868375, 2.23941517,
-0.7016392 , -0.75365341, 0.3458369 , -1.09171746, 1.19271684,
0.07945535, 0.13771758, 1.15739852, -1.08806617, -0.7665826 ,
-1.29355613, 0.72018477, -0.49924081, -0.93643934, -1.00544145,
1.1118645 , -0.42965894, 0.879536 , 0.40060254, -1.04417166,
0.77200148, 0.65680009, 0.61177494, 1.0622201 , 1.29132315,
0.79713301, 0.3011474 , 0.64205807, -0.96367853, -0.91645682,
0.17813906, 0.68752781, 0.35641676, -0.29888325, 1.2615063 ,
-0.25650754, -1.87887921, -1.28345256, 0.05882579, 1.49113695,
0.64879919, -1.04886286, -0.08680253, -1.02739249, -0.25119126,
-0.7218675 , -0.63581296, -0.61223376, -0.57580404, -1.20087052,
-0.01721705, 0.88722105, -1.65392975, -0.56155685, -1.07593906,
0.47305601, -0.31929999, -0.67340951, 0.49928351, 0.42550937,
-1.04867572, -0.4893241 , 0.0611306 , -0.6252364 , -0.428681 ,
-0.31425925, 0.23643226, 0.00983502, -0.21713571, 1.28594723])
>>> s.mean()
-0.057984384797540277
>>> s.max()
2.2394151712752057
>>> s.min()
-1.87887921016916
>>> s.var()
0.66484939561623224
>>> s.std()
0.8153829748138185
>>> median(s)
-0.084932172153511315
>>> var(s)
0.66484939561623224
>>> var(s, ddof=1)
0.67156504607700229
>>> from scipy import stats
>>> stats.describe(s)
(100, (-1.87887921016916, 2.2394151712752057), -0.057984384797540277, 0.67156504607700229, 0.1199184494811838, -0.5524733472330245)
>>> n = stats.norm(loc=3.5, scale=2.0)
>>> n.rvs()
4.831272143178463
>>> n.rvs()
2.8861479633680927
>>> n.rvs(size=100)
array([ 2.11184939, 4.78165465, 4.12409628, 4.5026254 , 3.43577725,
3.08707195, 1.08559378, 4.43936556, -0.08060345, 0.11254478,
3.97356158, 2.99724993, 4.3711152 , 5.49200907, 5.13812998,
-0.33957203, -0.77464655, -0.27844991, -0.37933802, 1.28560726,
3.48797001, 4.16787746, 3.12217925, 4.21513224, 0.71591849,
3.8606024 , 0.33783606, 2.47740255, 2.85838788, 0.03450961,
-0.6361362 , 4.2122434 , 0.06084516, 1.67969954, 3.31455011,
4.40255746, 3.50529632, 0.55936595, 1.66843076, 2.21574165,
2.14045843, 0.29911356, 3.98899147, 5.2209135 , 3.09099967,
4.0916305 , 3.6033646 , 1.83276318, 1.35611439, 5.46559031,
6.73534857, 5.2327596 , 4.60828241, -1.6882662 , 5.57548435,
7.33423661, 0.88707396, 2.20646822, 4.44804549, 1.92187448,
1.20585576, 2.56594066, 5.25369073, 4.6100597 , 1.7517909 ,
1.98021973, -0.84243018, 3.50121971, 4.51619849, 5.26074887,
-0.33572785, 5.37461601, -1.32558684, 2.10987711, 4.07143877,
4.88234816, 4.66115453, 5.56711906, 2.67081842, 4.36641944,
6.57944382, 0.45365671, 6.99858181, 3.60578627, 6.40016184,
5.77376511, 2.91588904, 3.41166583, 7.36777987, 0.78873316,
7.58259791, 3.96921519, 1.98166742, 1.07761526, 0.07161138,
-0.25385144, 2.02653839, 2.93447523, 3.65707149, 1.56364379])
>>> stats.norm.pdf(0, loc=0.0, scale=1.0)
0.3989422804014327
>>> stats.norm.pdf([-0.1, 0.0, 0.1], loc=0.0, scale=1.0)
array([ 0.39695255, 0.39894228, 0.39695255])
>>> tries = range(11)
>>> print(stats.binom.pmf(tries, 10, 0.5))
[ 0.00097656 0.00976563 0.04394531 0.1171875 0.20507813 0.24609375
0.20507813 0.1171875 0.04394531 0.00976563 0.00097656]
>>> def binom_pmf(n=4, p=0.5):
... x = range(n+1)
... y = stats.binom.pmf(x, n, p)
... plt.plot(x,y,"o", color="black")
... plt.axis([-(max(x)-min(x))*0.05, max(x)*1.05, -0.01, max(y)*1.10])
... plt.xticks(x)
... plt.title("Binomial distribution PMF for tries = {0} & p ={1}".format(n,p))
... plt.xlabel("Variate")
... plt.ylabel("Probability")
... plt.draw()
...
>>> binom_pmf()
>>> binom_pmf()
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