# Risk and Pure Premium calculations?

“Bob’s income is $14,400. There is a %50 chance Bob will get sick during the next year. If Bob gets sick, he will incur a loss of $4,400. His utility function in U (I)=I^.5 (utility equals the square root of income).

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What is Bob’s expected income? What is Bob’s expected loss? What is Bob’s expected utility? What is the maximum amount of money Bob is willing to pay for insurance? What is the pure premium? What is the risk premium?”