69. 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 ln (E[ea X ])

where a is some specified positive constant. Find P when X is an exponential random variable with parameter λ, and a = αλ, where 0 <α< 1.