Let X1, X2, , Xn be i i d random variables following an exponential distribution with rate parameter 0 Define X(1) min(X1, X2, , Xn) as the minimum of these n random variables (a) Derive the probability density function (PDF) of X(1) (b) Compute the expected value E X(1)

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Let X1, X2,       , Xn be i i d random variables following an exponential distribution with rate parameter   0  Define X(1)   min(X1, X2,       , Xn) as the minimum of these n random variables  (a)  Derive the probability density function (PDF) of X(1)  (b)  Compute the expected value E X(1)

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Question: Let X1, X2, . . . , Xn be i.i.d random variables following an exponential distribution with rate parameter > 0. Define X(1) = min(X1,

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