3. Independence Blue Cross [25 points} independence Blue Cross (IEC) offers a traditional health insurance policy that reimburses policy holders for their medical expenses. The amount the policy pays a policy holder depends on the total dollar value of the medical claims slhe files in a given year. Reimbursement for annual medical claims works as follows. - if annual claims fall below a fixed deductlble limit of $1,000, the policy holder receives nothing. For example, a policy holder with $800 of annual claims receives nothing from ISO. - Beyond the $1,000 deductible limit, the policy reimburses 80% of expenses, up to a co-pay limit of $6,000. For example, with annual claims of $1,500, a policy holder would receive $400 = 80% * ($1 ,500 - $1 ,000) from IBC. - Annual claims beyond the $8,000 co-pay limit are reimbursed at 100%. For example, a policy holder with $?,000 of annual claims would receive $5,000 = 80% ' [$6,000 - $1,000) + 100% ' ($T,000 - $8,000) from IBC. IEIC's policy holders' annual medical claims are independent and identically distributed (Ltd) and are lognormally distributed with a mean of $4,000 and a standard deviation of $2,000. a) {4 points} Let E be a random variable that represents a policy holder's annual medical expenses in $. Write one or more mathematical expressions to define his or her payout in $ from the policy (P) as a function of E. Note: for thls problem you may use Excel or Excel-like statements such as \"ll", \"min\