33. The monthly wholesale price and quantity sold of fresh squeezed orange juice during the winter months

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33. 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 pð Þ¼ ; q :01pe:01pqI½ 1:50;2:50 ðpÞI½ Þ 0;1 ðqÞ

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 ¼ PQ.

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

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

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