The lifetime in hours of a certain kind of radio tube is a random variable with the probability density function given by

fx(x)= { 0 ,x<=100}

{ 100/x^2, x>100 }

a) What is the probability that a radio tube will need to be replaced in the first 150 hours of operation?

b) There are 5 tubes in a radio set. What is the probability that exactly 2 of the 5 tubes will need to be replaced within the first 150 hours of operation?

c) What is the probability that a single radio tube will last between 200 and 500 hours?

d) The technician knows that a single radio tube lasted 1000 hours to this point. What is the probability that the tube will last no more than another 750 hours?