The Rayleigh density function is sometimes used by engineers to model lengths of life of electronic components and is given by: (²) e-y²/0 f(y)= y>0 elsewhere (a) Find E(Y). (b) If Y has the Rayleigh density, find the probability density function for U = Y² using the transformation method. Explain why the transformation method can be used for U-Y2 even though h(y) = y² is not monotonic over the entire real line. (Hint: do we need to account for P(Y y) for y ≤ 0?) (c) Find V(Y) using your answer in parts (a) and (b) (i.e. calculate E(U)).

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