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 hgigher 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?