(solution) Sum of a geometric number of independent geometric random variables. Let Y = X 1 + … + X N ….

(solution) Sum of a geometric number of independent geometric random variables. Let Y = X 1 + … + X N ….

Sum of a geometric number of independent geometric random variables. Let Y = X1 + … + XN . where the random variables X, are geometric with parameter p. and N is geometric with parameter q. Assume that the random variables N, X1 . X2 . . .. are independent. Show. without using transforms, that Y is geometric with parameter pq. Hint: Interpret the various random variables in terms of a split Bernoulli process.