This problem is intended as practice for induction proofs. See, for example, page 18 of (CF) for a definition of the Erlang distribution. We will use mathematical induction to prove the following statement: "Let X, for i = 1, 2..., n be n i.i.d. Exponentially distributed random variables with parameter 1. Then, Y = ; i=1 follows an Erlang distribution with shape parameter k = n and scale parameter 3 = * " (a) Show that the statement above holds if n=2. Hint: use convolution. (b) Assume the statement above is true for n-1 exponential random variables. Use that assumption to show that it holds for n exponentials. Hint: use convolution