Good day There is a question where we are given X ~ chi_square(m), Y ~ chi_square(n) and we need to use convolution to show that X + Y ~ chi_square(m+n). On the memo they use the substitution t = x/z and the upper bound of the integral changes from z to 1. How did they get to change that z to a 1 because I do not understand that part? I guess it makes sense because the integral just evaluates to a Beta pdf but I just do not understand how the z changes to a 1. Best
Hi Thabo I am assuming this is from practice question 4.10, the limits of x go from 0 to z, so the limits of t go from 0 to 1, as t=x/z the upper limit of t is z/z, which is where the 1 is from.
