Question

A dishonest used-car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown within the next 6 months. The dealer provides a warranty of 45 days (i.e. 1.5 months) on all cars sold. Let x represent the length of time until the breakdown occurs. Assume that x is a uniform random variable with values between 0 and 6 months.

a. Calculate and interpret the mean of x.

b. Calculate and interpret the standard deviation of x.

c. Find the probability density function (pdf).

d. Calculate and interpret the probability that the breakdown occurs while the car is still under warranty.

Answer 1