Transformations of Two Random Variables

Abstract

Problem : (X,Y ) is a bivariate rv. Find the distribution of Z = g(X,Y ). • The very 1st step: specify the support of Z. • X,Y are discrete – straightforward; see Example 0(a)(b) from Transformation of Several Random Variables.pdf. • X,Y are continuous – The CDF approach (the basic, off-the-shelf method) – Special formula (convolution) for Z = X + Y – MGF approach for sums of multiple independent rvs.