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An insurance company offers a particular kind of policy whereby the insured person pays a premium of $200 and thereby becomes eligible to receive
An insurance company offers a particular kind of policy whereby the insured person pays a premium of $200 and thereby becomes eligible to receive compensation in the event of a particular kind of accident whose probability of occurring during the policy period is 100p%. The policy will pay the costs arising from the accident, assumed to be exponential with mean $900, but only that part of the costs in excess of $500, and only up to a maximum payout of $4,000. Assume that at most one accident can occur.
(a) Find α, the probability that a policy holder will incur an overall loss over the policy period of more than $2,000, taking into account the premium and costs associated with the potential accident. Also, find β, the probability that a person without the policy (but subject to the same risks as a policy holder) will incur an overall loss over the same period of more than $2,000, taking into account the costs associated with the potential accident. Express α and β as functions of p. Then evaluate α and β when p=0.03.
