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10pts) Let Y be a continuous random variable with density function f(y) = 1 2 e...

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 ).

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Answer #1

The pdf is given by:


The MGF is given by E(etY)











Thus, for |t| < 1,



Hence, the variance is:







Hence, Var(Y) = 2.

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