probabiltiy_distributions.py

import scipy.stats as stats
import numpy as np

## Exercise 1
# sampling from a 6-sided die
die_6 = range(1, 7)
print(np.random.choice(die_6, size = 5, replace = True))


## Exercise 4 - binomial probability mass function
# 6 heads from 10 fair coin flips
print(stats.binom.pmf(6, 10, 0.5))


## Exercise 6 - binomial probability mass function
# 2 to 4 heads from 10 coin flips
# P(X = 2) + P(X = 3) + P(X = 4)
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))

# 0 to 8 heads from 10 coin flips
# 1 - (P(X = 9) + P(X = 10))
print(1 - (stats.binom.pmf(9, n=10, p=.5) + stats.binom.pmf(10, n=10, p=.5)))


## Exercise 9 - binomial cumulative distribution function
# 6 or fewer heads from 10 coin flips
print(stats.binom.cdf(6, 10, 0.5))

# more than 6 heads from 10 coin flips
print(1 - stats.binom.cdf(6, 10, 0.5))

# between 4 and 8 heads from 10 coin flips
print(stats.binom.cdf(8, 10, 0.5) - stats.binom.cdf(3, 10, 0.5))


## Exercise 10 - normal distribution cumulative distribution function
# stats.norm.cdf(x, loc, scale)
# temperature being less than 14*C
  # x = 14, loc = 20, scale = 3
print(stats.norm.cdf(14, 20, 3))


# Exercise 11
# temperature being greater than 24*C
  # x = 24, loc = 20, scale = 3
print(1 - stats.norm.cdf(24, 20, 3))

# temperature being between 21*C and 25*C
  # x = 24, loc = 20, scale = 3
print(stats.norm.cdf(25, 20, 3) - stats.norm.cdf(21, 20, 3))