In [3]:

    

import numpy as np


    

In [4]:

    

def simulation(f, rounds):
    values = [
        f()
        for _ in xrange(rounds)
    ]
    return np.var(values)


    

In [5]:

    

def a():
    x = np.random.normal(size=50)
    y = np.random.normal(size=50)
    return np.mean(x) - np.mean(y)


    

In [6]:

    

simulation(a, 10000)


    

    
Out[6]:





0.040377318794359872

In [7]:

    

def b():
    x = np.random.choice(np.random.normal(size=100), 50, replace=False)
    y = np.random.choice(np.random.normal(size=100), 50, replace=False)
    return np.mean(x) - np.mean(y)


    

In [8]:

    

simulation(b, 10000)


    

    
Out[8]:





0.039048497384724296

In [9]:

    

def c():
    x = np.random.choice(np.random.normal(size=100), 50, replace=True)
    y = np.random.choice(np.random.normal(size=100), 50, replace=True)
    return np.mean(x) - np.mean(y)


    

In [10]:

    

simulation(c, 10000)


    

    
Out[10]:





0.059948939898851972

In [11]:

    

def d():
    p = np.random.normal(size=100)
    x = np.random.choice(p, 50, replace=False)
    y = np.random.choice(p, 50, replace=False)
    return np.mean(x) - np.mean(y)


    

In [12]:

    

simulation(d, 10000)


    

    
Out[12]:





0.019564752456811486

In [13]:

    

def e():
    p = np.random.normal(size=100)
    x = np.random.choice(p, 50, replace=True)
    y = np.random.choice(p, 50, replace=True)
    return np.mean(x) - np.mean(y)


    

In [15]:

    

simulation(e, 10000)


    

    
Out[15]:





0.039312577910830447