Problem 1 10 marks 5 5 Let Y1 and Y2 be independent Geometri

Problem 1. (10 marks; 5, 5) Let Y1 and Y2 be independent Geometric random variables
with parameter p.
a) Show that W = Y1 + Y2 has a Negative Binomial Distribution with parameters r = 2 and p.

b) Let U1 and U2 be independent Uniform random variables in (0; 1). Using U1, U2, and part a); propose a \"transformation\" to generate Wpart a.