Find the cdf and pdf for the product of u and v the first

Suppose that U and V are iid Exp(1), i.e. have joint pdf

f(u,v)=I[0<u<1 and 0<v<1]exp(-(u+v))

Find the cdf and pdf for the product of U and V. (The first will require computaion of a double integral over an appropriate (u,v) region.)

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