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