In: Math
Let X ~ exp(λ)
MGF of X = λ/(1-t)
a) What is MGF of Y = 3X
b) Y has a common distribution, what is the pdf of Y?
c) Let X1,X2,....Xk be independent and identically distributed with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below the summation symbol, and k is on top of the summation symbol). What is the MGF of S?
d) S has a common distribution. What is the pdf of S?