Chapter 3.1, Problem 17E

An insurance agent receives a bonus if the loss ratio L on his business is less than 0.5, where L is the total losses (say, X) divided by the total premiums (say, T). The bonus equals $\left(0.5-L\right)\left(T/30\right)$ if $L<0.5$ and equals zero otherwise. If X (in $100000) has the pdf $f\left(x\right)=\frac{3}{x^4},x>1$, and if T (in $100,000) equals 3, determine the expected value of the bonus.