The monthly wholesale price and quantity sold of fresh squeezed orange juice during the winter months by a small Florida growers' cooperative is represented by the following bivariate probability density function:

\(F(p, q)=.01 p e^{-.01 p q} I_{[1.50,2.50]}(p) I_{[0, \infty)}(q)\) where \(p\) is measured in dollars per gallon and \(q\) is measured in 1,000 's of gallons.

(a) Derive the probability density function of total revenue, \(R=P Q\).

(b) What is the expected value of total monthly revenue?

(c) What is the probability that total monthly revenue exceeds \(\$ 100,000\) ?