The percentage of alcohol in a certain compound may be considered as a random variable X with the following pdf
fX (x) = 20x^3 (1 - x), 0 < x < 1.
Suppose that the selling price of the above compound depends on the alcohol contents. Specifcally, if 1/3 < X < 2/3, the compound sells for 120 dollars/gallon otherwise it sells for 90 dollars/gallon. If the cost is 50 dollars/gallon, and the probability distribution of the net profit per gallon.