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Let X Exp(x) and X Exp(X2) be independent exponential random variables. (a) When X X2, determine the probability density function of X + X.

   

Let X Exp(x) and X Exp(X2) be independent exponential random variables. (a) When X X2, determine the probability density function of X + X. (b) Determine the probability density function of max(X, X2). (c) Determine E[max(X, X)]. (d) Determine P(X < X). [5] [5] [5] [5]

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