Self Made[Variation to Gate 2004 Ques]

Question

Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively.

If Z = MAX (X,Y), then the mean of Z is given by

Comments

Following the procedure there I got,

$P(Z \geq a) = e^{-a/ \alpha} + e^{-a/ \beta} +e^{-a/ \alpha -a/ \beta}$

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What will be mean for that ..i think it is bit calculative than MIN rt ?

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Yes i think so..