A store manager is very impatient at the start of the day. Let X be the time (in minutes) until his first customer arrives. The workers at the store decided to find a way to measure his impatience level as a function of X:
g(X) = aX2 + bX + c,
Where a, b, c are fixed constants.
a. Calculate the manager's expected impatience level.
b. Find the variance of the manager's impatience level.