Let X be the number of the cars being repaired at a repair shop. We have the following information: At any time, there are at most 3 cars being repaired.
The probability of having 2 cars at the shop is the same as the probability of having one car.
The probability of having no car at the shop is the same as the probability of having 3 cars.
The probability of having 1 or 2 cars is half of the probability of having 0 or 3 cars.
(a) What is the sample space?
(b) Find the pmf of X and draw the histogram of pmf.
(c) Find the cdf of X and draw the histogram of cdf.