A car dealer offers two cars A and B at the same price. The lifetimes of cars A and B are denoted by X and Y, respectively. Assume X is uniformly distributed over the interval [5,50] (in thousands of miles), and Y is exponentially distributed with parameter =1/25.

a) You want the car with the greater probability of operating 35,000 miles. Which one do you choose?

b) Which car has the longer expected lifetime?

c) Assume that both cars have been driven 15,000 miles. What is the probability that the owner would get at least 30,000 additional miles from car A ? Repeat the same for car B.