The Binominal Distribution

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.
It is represented as B(n, p), with n being the fixed number of trials and p as the probability of success per trial.
Key assumptions include each trial being independent and yielding only two outcomes (success or failure).
Its probability mass function is given by P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where X is the number of successes and C(n,k) outlines the number of combinations of n items taken k at a time.
Useful statistical properties such as the mean (μ = np) and variance (σ^2 = np(1-p)) can be derived from the binomial distribution.