Expected value of a random variable is the weighted average

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Jamal has a utility function U=(w^1/2) , where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 Million for sure, or (B) a gamble that pays $1 million with a probability of 60% or $9 million with a probability of 40%.

A. Graph Jamal's function. Is he risk averse? Explain.

B. Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (HINT: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)

C. Does A or B offer Jamal a higher expected utility? Again, show your calculations.

D. Should Jamal pick A or B? Why?

Reference no: EM13737821

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