# hw-10 - 1 Random Variable Probability \$0 98 \$30,000 2 a AFP...

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1. Random Variable Probability \$0 98% \$30,000 2% a. AFP = 0*(.98) + 30,000*(.02) = \$600

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The Actuarially Fair Premium (AFP) Manaka Insurance will charge Rachel is \$600. b. Manaka insurance will face the same risk as Rachel. When there is a single exposure unit in the risk pool, there would be no risk reduction. 2. a. Condition Loss Calculation P[Loss] K NOLOSS R NOLOSS \$0 (.50)*(.50) .25 K NOLOSS R LOSS \$30,000 (.50)*(.50) .25 K LOSS R NOLOSS \$30,000 (.50)*(.50) .25 K LOSS R LOSS \$60,000 (.50)*(.50) .25 Combined Probability Loss P[Loss] \$0 .25 \$30,000 .50 \$60,000 .25 b. The Expected Loss for Manaka Insurance if they sell contracts to both Rachel and Keith is \$30,000. 0*(.25) + 30,000*(.50) + 60,000*(.25) = \$30,000 c. Individual with Insurance EL= \$600 Variance= [(0-600) 2 x .98) + (30,000-600) 2 x .02)] = 17,640,000 Standard Deviation= square root of 17,640,000 = 4,200 Coefficient of Variation = 4,200/600= 7.0 Two Person Pool EL= \$30,000 Variance= [(0-30,000) 2 x .25) + (30,000-30,000) 2 x .50) + (60,000-30,000) 2 x .25) = 450,000,000\$ 2 Standard Deviation= square root of 450,000,000 Coefficient of Variation = square root of 450,000,000/30,000 = 0.707 By having more than one person in the risk pool, the overall risk decreases as measured by the coefficient of Variation. As the risk pool gets larger, the risk for the
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