Cumulative Distribution Function (cdf)

import scipy.stats as stats

# Using Cumulative function as a faster way to calculate than pmf

# probability of observing 3 or fewer heads from 10 fair coin flips
# P(3 or fewer heads)=P(0 to 3 heads)
prob_1 = stats.binom.cdf(3, 10, 0.5)
print(prob_1)

# compare to pmf code - add each from 0 to 3
print(stats.binom.pmf(0, n=10, p=.5) + stats.binom.pmf(1, n=10, p=.5) + stats.binom.pmf(2, n=10, p=.5) + stats.binom.pmf(3, n=10, p=.5))

# probability of observing more than 5 heads from 10 fair coin flips (use 1 minus) - want from 6 to 10
# P(more than 5 heads)= 1 − P(5 or fewer heads)
prob_2 = 1- stats.binom.cdf(5, 10, 0.5)
print(prob_2)

# probability of observing between 2 and 5 heads from 10 fair coin flips
# P(2 to 5 Heads)=P(0 to 5 Heads)−P(0 to 1 Heads)
prob_3 = stats.binom.cdf(5, 10, 0.5) - stats.binom.cdf(1, 10, 0.5)
print(prob_3)

# compare to pmf code - add each from 2 to 5
print(stats.binom.pmf(2, n=10, p=.5) + stats.binom.pmf(3, n=10, p=.5) + stats.binom.pmf(4, n=10, p=.5) + stats.binom.pmf(5, n=10, p=.5))