Find the moment generating function of x

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Reference no: EM13909713

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.

Reference no: EM13909713

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