The warranty on a machine specifies that it will be replaced

The warranty on a machine specifies that it will be replaced at failure or at age 3, whichever occurs first. The machine’s age at failure, X, has probability density function f(x) = c/x^3 , if x > 1, 0, otherwise, for some constant c. Let Y be the age of the machine at the time of replacement. Determine the expected value and variance of Y .

Solution