Recall that if X1,...,Xk are independent random variables
Chapter 4, Problem 4.3.2(choose chapter or problem)
Recall that if X1,...,Xk are independent random variables each having an exponential distribution with parameter , then the random variable X = X1 ++Xk has a gamma distribution with parameters k and .(a) Use this fact to verify the expectation and variance of a gamma distribution. Check that you get the same answer for the expectation of a gamma random variable using the formula E(X) = 0 xf (x) dx where f (x) is the probability density function of the gamma distribution. (b) If X has a gamma distribution with parameters k1 and , and Y has a gamma distribution with parameters k2 and , where k1 and k2 are both positive integers and X and Y are independent random variables, explain why Z = X +Y has a gamma distribution with parameters k1+k2 and.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer