# Problem utilizing order statistics

• Jan 25th 2011, 04:29 PM
jmyers12345
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.
• Jan 25th 2011, 06:59 PM
mr fantastic
Quote:

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.

Calculate the pdf of $W = Y_{(1)}$ and use it to calculate the mean of W.