1 you have 80 dollars and play the following game an urn, Ask an Expert

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1. You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. What is your expected final fortune?

2. In the hat check problem (see Example 3.12), it was assumed that N people check their hats and the hats are handed back at random. Let Xj = 1 if the jth person gets his or her hat and 0 otherwise. Find E(Xj ) and E(Xj · Xk ) for j not equal to k. Are Xj and Xk independent?

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