Problem utilizing order statistics

Hello all. The problem statement is as follows:

Consider a system containing n components where the lifetimes of the compoenets are independent random variables and each has pdf f_y(y) = λe^(-λy), y > 0. Show that the average time elapsing before the first component failure occurs is 1/nλ

I'm not really sure where to go with this problem. I feel that I should first find the pdf of the order statistic Y_(1), but I'm not sure where to go after that. Any help is appreciated.

Quote:

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Originally Posted by jmyers12345

Hello all. The problem statement is as follows:

Consider a system containing n components where the lifetimes of the compoenets are independent random variables and each has pdf f_y(y) = λe^(-λy), y > 0. Show that the average time elapsing before the first component failure occurs is 1/nλ

I'm not really sure where to go with this problem. I feel that I should first find the pdf of the order statistic Y_(1), but I'm not sure where to go after that. Any help is appreciated.

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Calculate the pdf of and use it to calculate the mean of W.