(11) Prove that (a) sum of r independent geometric random variables each with parameter p is a negative binomial random variable with the parameters (r,p). (b) the sum of two independent binomial random variables with the parameters (n,p) and n,p) is a binomial random variable with the parameters (n + n, p). 1 (c) sum of two independent Poisson random variables with the parameters A1 and A2 is a Poisson random variable with the parameter A1 + A2.. (d) sum of r independent exponential random variables each with the parameter is a gamma random variable with the parameters (r. B). (e) sum of two independent gamma random variables with the parameters (a1, B) and (2, 3) is a gamma random variable with the parameters (a + a2, B). (f) sum of two independent x-random variables with n and no degrees of freedom is a x-random variable with n + n degrees of freedom. (g) any linear combination of two independent normal random variables is again a normal random variable. == (12) If the pdf of X is f(r) = 2re, r>0, zero elsewhere, determine the pdf of Y = X. (13) Let f(r), -1