STAT330 Lecture Notes - Lecture 12: Marginal Distribution, Partial Derivative

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Reza

Document Summary

Last class: discrete random variables, joint probability distributions (cont"d, properties of joint p. m. f, marginal distributions, independence. Today: continuous random variables, joint probability distributions, properties of joint p. d. f, marginal distributions, independence, conditional distribution introduction. De nition: two random variables x and y are said to be jointly continuous if there exists a function f (x, y ) such that the joint. C. d. f. of x and y can be written as follows. Z y f (t1, t2) dt2 dt1, (x, y ) r2. The function f (x, y ) is called the joint density function of x and. It follows from the de nition above that when the second order partial derivative exists, f (x, y ) = Convention: de ne f (x, y ) = 0 when 2. X y f (x, y ) does not exist. The set {(x, y ) : f (x, y ) > 0} is called the support set of (x,y).