Question: 3.8* Exponential function of an exponential RV. For Z = e, where a > 0 and X is an exponentially distributed RV with the PDF

3.8* Exponential function of an exponential RV. For Z = e", where a > 0 and X is an exponentially distributed RV with the PDF given by (3.55). Find (a) the PDF of Z and (b) the mean and variance of Z. wapu A RV X has the exponential PDF f(x) = >e Vu(x) A>0 u(x) = unit step function (3.55) where the factor A is necessary to guarantee , f(r)dr = 1. f(z) Figure 3.21: The PDF of an exponentially-distributed RV.\f(b) Mean and Variance of Z: 1. Mean of Z: These formulas provide the mean and variance of Z in terms of the parameters ) and a

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