A small domestic manufacturer of television sets places a three-year warranty on its picture tubes. During the warranty period, the manufacturer will replace the television set with a new one if the picture tube fails. The time in years until picture tube failure can be represented as the outcome of a random variable \(X\) with probability density function

\(f(x)=.005 e^{-.005 x} I_{(0, \infty)}(x)\).

The times that picture tubes operate until failure can be viewed as independent random variables. The company sells 100 television sets in a given period.

(a) What is the expected number of television sets that will be replaced due to picture tube failure?

(b) What is the expected operating life of a picture tube?