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Bernoulli Variable

Bernoulli Variable

In this lesson, we will learn about finding the probability of a Bernoulli variable.

We'll cover the following...

In the example below, we will flip a coin five times in a row and record how many times we obtain tails (varying from 0-5). We will be performing the experiment 1000 times.

We will then compute the cumulative probability, print the values to the screen and make a plot of the cumulative probability function using a bar graph.

Python 3.5
import numpy as np
import matplotlib.pyplot as plt
import numpy.random as rnd
N = 1000
tails = np.sum(rnd.randint(0, 1+1, (5, 1000)), axis=0)
counttails = np.zeros(6, dtype='int')
for i in range(6):
    counttails[i] = np.count_nonzero(tails == i)
prob = counttails / N
cum_prob = np.cumsum(prob)
print('probababilties:', prob)
print('cumulative probabilities:', cum_prob)
plt.bar(range(0, 6), cum_prob)
plt.xticks(range(0, 6))
plt.xlabel('number of tails in two flips')
plt.ylabel('cumulative probability');

Execute the code several times and see that the graph changes a bit every time.

Probability of a Bernoulli variable

In the example above, we computed the probability of a certain number of heads in five flips experimentally. But we can, of course, compute the value exactly by using a few simple formulas.

Consider the random variable YY, which is the outcome of an experiment with two possible values 00 and 11. Let pp be the probability of success,

p=P( ...