Theorem 5.2.9 (Convolution formula) : Let X and Y are independent continuous random variables with pdfs fX(X) and /(y), then the pdf of Z : X + Y is rziz) : f ems/(z w)dw Note : For next theorem, we need to recall the following facts : 0 When we have a sum of the squares of n independent standard normal r.vs, it follows xi where n is the degrees of freedom 0 As a special case, in example 2.1.9, we derived a pdf of xi 0 XE: distribution has Mx(t) : (1/(1 7 2H)? (Verify this!) 0 Independent chisquared variables add to a chisquared variable, and the degrees of freedom also add