The percentage of alcohol in a certain compound is a random variable Y , with the
Chapter 6, Problem 6.109(choose chapter or problem)
The percentage of alcohol in a certain compound is a random variable Y , with the following density function: f (y) = $ 20y3(1 y), 0 < y < 1 0, otherwise. Suppose that the compounds selling price depends on its alcohol content. Specifically, if 1/3 < y < 2/3, the compound sells for C1 dollars per gallon; otherwise, it sells for C2 dollars per gallon. If the production cost is C3 dollars per gallon, find the probability distribution of the profit per gallon.
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