Two insurance policies, G and H, can each only submit one claim in a given month. For insurance policy G, there is a 45% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 5. For insurance policy H, there is a 35% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 9. For both policies, there is a deductible of 2 and they only reimburse 80% of the amount that exceeds the deductible. Calculate the difference between the expected reimbursements of the two policies for a given month.

the difference between the expected reimbursements of the two policies for a given month is 2.32

Step-by-step explanation:

Given That,

P (no claim in G) = 0.45

P (claim in G) = 1-0.45 = 0.55

P (no claim in H) = 0.35

P (claim in H) = 1-0.35 = 0.65

mean reimbursement = (mean claim - 2) * 0.80

mean reimbursement (G) = (5 - 2) * 0.80 = 2 ... 4

mean reimbursement (H) = (9 - 2) * 0.80 = 5.6

E (reimbursements) = P (claim) * (mean reimbursement)

E (reimbursements (G)) = P (claim in G) * (mean reimbursement (G))

= 0.55*2.4 = 1.32

E (reimbursements (H)) = P (claim in H) * (mean reimbursement (H))

= 0.65*5.6 = 3.64

difference in expected reimbursements = 3.64 - 1.32

difference in expected reimbursements = 2.32

Therefore, the difference between the expected reimbursements of the two policies for a given month is 2.32