In Self-Test Problem1, how many components would one need to have on hand to be approximat...

In Self-Test Problem1, how many components would one need to have on hand to be approximately 90 percent certain that the stock would last at least 35 days?

Problem1

The amount of time that a certain type of component functions before failing is a random variable with probability density function

f(x) =2x     0 < x < 1

Once the component fails, it is immediately replaced by another one of the same type. If we let Xi denote the lifetime of the ith component to be put in use, then represents the time of the nth failure. The long-term rate at which failures occur, call it r, is defined by

Assuming that the random variables Xi, i ≥ 1, are independent, determine r.