Let R have the Rayleigh density given by f(r) = re^(-1/2*r^2) for r>0.

In what follows, Z is standard normal.

a) Let F be the cdf of R . Find F(r) for r>0 by writing the integral for it.

b) Use the mean and variance of Z to find  E(R) without any further integration.

c) Use properties of R^2 to find E(R^2) without any further integration, and hence find Var(R).

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