2. (Modified from Question 3 of Chapter 3) Assume that property losses for Bucke

Question

2. (Modified from Question 3 of Chapter 3) Assume that property losses for Buckeye Brewery have the following distribution Probability 0.004 0.010 0.026 Loss $3,000,000 1,500,000 800,000 0.96 A. Answer the following questions: i. What is the expected value of the loss? ii. What is the standard deviation of the loss? B. Greater American Insurance Group underwrites the property risk from Buckeye Brewery. The policy involves a deductible of $300,000. The premium that Greater American charges is $50,000. Is this premium actuarially fair? Justify your answer with the calculation? C. Suppose the premium in (2) is not actuarially fair and suppose Buckeye Brewery is willing to purchase the coverage. Provide the rationale to Buckeye Brewery's purchase decision. D. What is the law of large number (LLN)? Why do people consider it as the cornerstone of the insurance business? E. Even with LLN, why are insurance premiums typically not actuarially fair?

Explanation / Answer

Dear there is a limited time on chegg to solve every question and also it is a policy of chegg to answer one question at once so please ask others as a seperate question

Solution (figures in millions) Probabity Loss 0.004 3 0.012 0.01 1.5 0.015 0.026 0.8 0.0208 0.96 0 0 Expected Loss    = (0.004*3) + (0.01*1.5) + (0.026*0.8) + (0.96*0) Expected Loss    = 0.0478 Standard deviation Probabity Loss Devation From Expected Squared Prob*Squared 0.004 3 ( 3-0.0478) = 2.9522 8.7155 0.03486 0.01 1.5 (1.5 - 0.0478) = 1.4522 2.1089 0.02109 0.026 0.8 (0.8 - 0.0478) = 0.7522 0.5658 0.01471 0.96 0 (0 - 0.0478) = -0.0478 0.0023 0.00219 VARIANCE    = 0.07286 Standard Deviation is the root of variance   =    (0.07286)1/2 0.2699

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