69. In deciding upon the appropriate premium to charge, insurance companies sometimes use the exponential principle, defined
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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 Image where a is some specified positive constant. Find P when X is an exponential random variable with parameter λ, andI mage, where Image.
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