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.