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You roll a fair 6-sided die once and observe the result which is shown by the...

You roll a fair 6-sided die once and observe the result which is shown by the random variable X. At this point, you can stop and win X dollars. Or, you can also choose to discard the X dollars you win in the first roll, and roll the die for a second time to observe the value Y. In this case, you will win Y dollars. Let W be the number of dollars that you win in this game.

a) What strategy do you use to maximize E[W]? What is the maximum E[W] you can achieve using your strategy?

b) If you have to pay the price of 1 dollar to do a second roll, i.e., you win Y−1 dollars if you choose to roll the die a second time. Will you change your strategy? Why?

Math   Statistics-And-Probability   
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