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 (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.

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