Question 3 Let X~ Gamma(a, B) be a Gamma random variable. That is, fx (2) = 0, I<0. Consider the reciprocal variable, Y = x. %3D (a) Consider the cumulative distribution function (cdf) ofY, Fy(y). Write Fy (y) in terms of the cdf of X, Fx- (b) Verify that the cdf you derived above is a valid cdf. (c) Consider the probability density function (pdf) of Y, fy(y). Show that the pdf of Y is, y> 0; fy (y) = {ay %3D y< 0. (d) Verify that the pdf above is a valid pdf.

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