a) Find the Erlang density fS n (t) by convolving fX(x) = λ exp(-λx) with itself n times. b) Find the moment generating function of X (or find the Laplace transform of fX(x)), and use this to find the...

b) Find the moment generating function of X (or find the Laplace transform of fX(x)), and use this to find the moment generating function (or Laplace transform) of S_n
= X₁
+ X₂
+ · · · + X_n. Invert your result to find fSn (t).

c) Find the Erlang density by starting with (2.15) and then calculating the marginal density for S_n.