The warranty on a machine species that it will be replaced a

The warranty on a machine species 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