Probability Mass Function (PMF)

Definition

The PMF is a function that gives us probabilities associated with specific values of discrete random variables. It assigns probabilities to all possible outcomes and satisfies two properties: each probability is between 0 and 1, and the sum of all probabilities is equal to 1.

Analogy

Imagine you have a bag of colored marbles. The PMF would be like a chart that tells you the probability of picking each color from the bag.

Related terms

Geometric Distribution: A probability distribution that models the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials with the same probability.

Binomial Random Variable: A random variable representing the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.

Cumulative Distribution Function (CDF): A function that gives the cumulative probabilities for all values less than or equal to a given value for a discrete or continuous random variable.