Question

(Need solution for part b) You are offered to play the following game. 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 the game 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.

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?

part a) was

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

Answer 1