The Lifetime in hours of a certain kind of radio tube is a r

The Lifetime in hours of a certain kind of radio tube is a random variable having probability density function: f(x) = 100/x2; x > 100 What is the probability that exactly 2 of 5 such tubes in a radio set will have to be replaced within the first 150 hours of operation? Assume that the events Ei, i = 1, 2, 3, 4, 5 that the ith such tube will have to be replaced within this time are independent.

Solution

f(x) = 100/x^2 for x >100

we have to find the probability of replacing 2 of 5 will be equal to the two tube withstand / maximum 5 tube can withstand in hours .

according to the function 5 tubes can withstand = (100/x^2)^5

2 tube can withstand = (100/x^2)^2

dividing both we will get the probability be (1/100)^3