In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined as foll
ows. With X as the random amount that it will have to pay in claims, the premium charged by the insurance company is P = 1/a ln(E(e aX )) where a is some specified positive constant. Find P when X is exponential random variable with parameter lambda, and a = alpha lambda, where 0 < alpha < 1.
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