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Expectation of min of exponentials

By in Expectations, Exponential Random Variables, Max and Mins on .

There are \(15\) stock brokers. The returns (in thousands of dollars) on each brokers is modeled as a separate independent exponential distribution \(X_1 \sim \mbox{Exp}(\lambda_1),…,X_{15} \sim \mbox{Exp}(\lambda_{15})\). Define \(Z = \min\{X_1,…,X_{15}\}\).

What is \(\mathbf{E}(Z)\) ?

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