The proportion Y of a data processing company’s yearly hardware repair budget allocated to repair its laser color printer has an approximate beta distribution with parameters α = 2 and β = 9.
a. Find the mean and variance of Y.
b. Compute the probability that for any randomly selected year, at least 40% of the hardware repair budget is used to repair the laser color printer.
c. What is the probability that at most 10% of the yearly repair budget is used for the laser color printer?