Question

10pts) Let Y be a continuous random variable with density function f(y) = 1 2 e −|y| , −∞ < y < ∞ 0, elsewhere (a) Find the moment-generating function of Y . (b) Use the moment-generating function you find in (a) to find the V (Y ).

Answer #1

The MGF is given by E(etY)

Thus, for |t| < 1,

Hence, the variance is:

Hence, Var(Y) = 2.

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