Calculate PMF, CDF, mean and variance for the binomial distribution B(n,p).
The binomial distribution B(n, p) models the number of successes in n independent Bernoulli trials, each with success probability p. It returns the exact probability of k successes (PMF) and the cumulative probability up to k (CDF).
P(X=k) = C(n,k) × p^k × (1−p)^(n−k)
When you have a fixed number of independent trials, each with the same probability of success, and you want the probability of a specific number of successes.
For large n, the binomial distribution can be approximated by a normal distribution with mean np and variance np(1−p).