Common probability distributionsI Math 217/218 Probability and Statistics

For each distribution, I give the name of the distribution along with one or two parameters and indicate whether it is a discrete distribution or a continuous one. Then I describe an example interpretation for a random variable X having that distribution. Each discrete distribution is determined by a probability mass function f which gives the probabilities for the various outcomes, so that f(x) = P (X=x), the probability that a random variable X with that distribution takes on the value x. Each continuous distribution is determined by a probability density function f , which, when integrated from a to b gives you the probability P (a ≤ X ≤ b). Next, I list the mean μ = E(X) and variance σ = E((X−μ)) = E(X)−μ for the distribution, and for most of the distributions I include the moment generating function m(t) = E(X ). Finally, I indicate how some of the distributions may be used.