Moments for Joint, Conditional, and Marginal Discrete Distributions

Free SOA Exam P (Probability) lesson in Multivariate Random Variables. 23 min read, ~3,453 words.

: double sum over the joint PMF. Iterated expectation:. is a random variable (a function of X); only collapses to the number. Eve's law:, total = within-group + between-group variance. ONLY when independent: otherwise compute from the joint. Covariance shortcut:. Linearity always holds, but the product rule and compound mean...