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 edf.