# Random Amount

62)In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined as follows. 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 In(E[e^ax])

where a is some specified positive constant. Find P when X is an exponential random variable with parameter (lambda), and a=a(lambda), where 0<(alpha)<1.

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#### Solution Summary

62)In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined as follows. 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 In(E[e^ax])

where a is some specified positive constant. Find P when X is an exponential random variable with parameter (lambda), and a=a(lambda), where 0<(alpha)<1.