Week 6: Discrete Probability Distributions - Binomial and Poisson distributions
Binomial Distribution Definition and Usage: The Binomial Distribution is a fundamental discrete probability distribution, typically used when considering a sequence of independent trials, each with two possible outcomes - commonly termed as success and failure. It's particularly useful in scenarios like coin flipping, quality control in manufacturing, or any process where the outcome is binary and probabilities remain constant. Parameters: n n : Total number of trials. p p : Probability of success on a single trial. q q or 1 − p 1 − p : Probability of failure on a single trial. Probability Mass Function: The probability of getting exactly k k successes in n n trials (where k k can be any number from 0 to n n ) is given by: P ( X = k ) = ( n k ) p k q n − k P ( X = k ) = ( k n ) p k q n − k This formula combines the binomial coefficient (which counts the number of ways to choose k k successes out of n n trials) with the probabilities of these successes and failures. Examp...