7 . Multivariate Probability

In the discrete case a joint probability mass function tells you the probability of any combination of events X = a and Y = b: pX ,Y (a,b) = P(X = a,Y = b) This function tells you the probability of all combinations of events (the “,” means “and”). If you want to back calculate the probability of an event only for one variable you can calculate a “marginal” from the joint probability mass function: pX (a) = P(X = a) = ∑ y PX ,Y (a,y) pY (b) = P(Y = b) = ∑ x PX ,Y (x,b)