Exercise 2.1
(a) Find the Erlang density f Sn (t) by convolving fX (x) = λ exp(-λx) with itself n times.
(b) Find the moment generating function (MGF) of X (or find the Laplace transform of fX (x)), and use this to find the moment generating function (or Laplace transform) of Sn = X1 + X2 + ··· + Xn. Invert your result to find fSn (t).
(c) Find the Erlang density by starting with (2.15) and then calculating the marginal density for Sn.
Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.