A supplier of kerosene has a weekly demand Y possessing a probability density function

Chapter 6, Problem 6.3

(choose chapter or problem)

A supplier of kerosene has a weekly demand Y possessing a probability density function given by

\(f(y)=\left\{\begin{array}{ll}
y, & 0 \leq y \leq 1 \\
1, & 1<y \leq 1.5 \\
0, & \text { elsewhere }
\end{array}\right.\)

with measurements in hundreds of gallons. (This problem was introduced in Exercise 4.13.) The supplier’s profit is given by \(U=10 Y-4\).

a Find the probability density function for U.

b Use the answer to part (a) to find E(U).

c Find E(U) by the methods of Chapter 4.

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