Exam P Univariate Distributions

Discrete Uniform PMF, E[X], Var[X], MGF

equally spaced finite number of values with equal probability

Bernoulli PMF, E[X], Var[X], MGF, PGF

probability of either success or failure

Bernoulli Shortcut

Binomial PMF, E[X], Var[X], MGF, PGF

number of successes in a number of n independent trials

Hypogeometric PMF, E[X], Var[X], MGF, PGF

number of successes m in a number of dependent trials

Geometric PMF, E[X], Var[X], MGF, PGF

number of trials to get first success

Negative Binomial PMF, E[X], Var[X], MGF, PGF

number of trials to get a specific number of successes

Poisson PMF, E[X], Var[X], MGF, PGF

Number of occurrences of an event during a fixed interval, where disjoint occurrences are independent

Continuous Uniform PMF, E[X], Var[X], MGF, PGF

continuous dist where every interval of the same length in domain is equally likely

Exponential Distribution PMF, E[X], Var[X], MGF, PGF

Used to model waiting times between independent events that occur with a constant average waiting time, theta

Gamma Distribution PMF, E[X], Var[X], MGF, PGF

Model waiting times between next alpha events

Normal Distribution PDF, E[X], Var[X], MGF