7.60 Let X be a continuous random variable with distribution function F(x) and density function f (x).

We can then write, for x1  x2, As a function of x2 for fixed x1, the right-hand side of this expression is called the conditional distribution function of X given that X x1. On taking the derivative with respect to x2, we see that the corresponding conditional density function is given by Suppose a certain type of electronic component has lifelength X with the density function (lifelength measured in hours)

Find the expected lifelength for a component of this type that has already been in use for 100 hours.