Question: 7.5. A certain alloy is formed by combining the melted mixture of two metals. The resulting alloy contains a certain percent of lead, say X,

7.5. A certain alloy is formed by combining the melted mixture of two metals. The resulting alloy contains a certain percent of lead, say X, which may be considered as a random variable. Suppose that X has the following pdf: f(x) = 10-5x(100 - x), 0 x 100. Suppose that P, the net profit realized in selling this alloy (per pound), is the following function of the percent content of lead: P = C + C2X. Compute the expected profit (per pound).

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