Distributions

A distribution assigns probabilities to every possible outcome of a random variable. For a fixed number of independent trials with two outcomes, use the binomial formula $P(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}$. For events occurring at a constant average rate over time, use the Poisson formula $P(X=k)=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$. For continuous outcomes over an interval, probability is the area under the density curve, found geometrically or by integration.