A small domestic manufacturer of television sets places a three-year warranty on its picture tubes. Dur ing 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) = .oose-·005x I10,001(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?