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3. Let U1, U2 be independent Uniform (0,1) random variables. (a) Let X = log(U1). Find the density function of X. - (b) Find

3. Let U1, U2 be independent Uniform (0,1) random variables. (a) Let X = log(U1). Find the density function of X. - (b) Find P(U + U > 1). (c) Find E[UI (U + U2) > 1)]. Here I() is the indicator function. (Hint: Use conditioning).

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