Question: Let A = UV, where U and V are independent and uniformly distributed on (0,1). (a) Find the density of A. (b) Find E[A] two

Let A = UV, where U and V are independent and uniformly distributed on (0,1).
(a) Find the density of A.
(b) Find E[A] two ways: 

(i) Using the density of A and 

(ii) Not using the density of A.

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