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Problem 5 An insurance company issues a policy on a car under the following conditions: (1) The replacement cost of $37,000 will be paid for a total loss. (ii) If it is not a total loss, but the damage is more than $11,000, then only $ 10,500 will be paid. (iii) Nothing will be paid for damage costing $11,000 or less and, (iv) Nothing will be paid out if there is no damage. The company estimates, based on their internal research, the probability of the first three events as 0.05, 0.15, and 0.25, respectively. a) Compute the expected amount paid out in a year. b) If the company wishes to make a profit of $200 a policy, what is the amount the company should charge per month?

Answer 1

Sal Lel x' be a Handom vouliable for the compony pay out in a Sal. year. X contarce the following & values i) The X = $31000 , if the cost of steplacement will be paid * = $ 10,500, if the damage is more than $ 11,000 but is not a total loss. 1) X = 0, is the damage costing is Jex than $1,000 (iv) x=0, if there is no damage. P( No damage) = 1-(0:05+0:15+0.25) = 0.55 So, P(x=$37000) = 0.05 P(X=$10500) = 0.15 P ( X = 0) = 0.55+0.25 = 0.80 So, The probability distribution of x'is as follows - X|37000 10500 O P(x) 0.05 0-15 0.80 @) E(X) = Ex.PLX) -${(37000x0.05 10-05)+(1 500 X0-5)+(0x0-80) - $3425 mu (6) Now, company wants to make a profit of $200 a policy, Total amount that company change in a yeay = $ (3425 +200) - $ 3625

So, Amount that company should charge per month = $[. 3625 12 $ 302.0833 my