Discrete Probability Distributions

A discrete probability distribution describes the probabilities of outcomes for a variable that can only take specific, countable values - such as the number of heads in 10 coin flips, or the number of customer complaints in a day.

Binomial Distribution

Models the number of successes in a fixed number of independent trials, each with the same probability of success - like counting heads across a fixed number of coin flips.

from scipy.stats import binom

# Probability of getting exactly 3 heads in 5 fair coin flips
p = binom.pmf(k=3, n=5, p=0.5)
print(p)

Poisson Distribution

Models the number of times an event occurs within a fixed interval of time or space, given a known average rate - like the number of customer support calls received per hour.

from scipy.stats import poisson

# Probability of receiving exactly 4 calls in an hour, if the average is 3 calls/hour
p = poisson.pmf(k=4, mu=3)
print(p)

Bernoulli Distribution

The simplest discrete distribution - models a single trial with only two possible outcomes, such as success/failure or pass/fail, each with a fixed probability.

Coming Up Next

Next, you'll look at continuous probability distributions, which apply when a variable can take any value within a range.