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Bill and Larry toss two coins. If both coins come up heads, Bill pays Larry $4. Larry pays Bill $1 otherwise. a. What is the expected value of this game for Bill? b. What is the expected value of this game for Larry? c. Bill and Larry play the game 100 times. Who should come out ahead and by how much? d. Bill and Larry play the game 100 times, and Larry comes out $23 ahead. Use only this empirical information to estimate the expected value of this game for Bill and the expected value for Larry. e. Explain the difference, in general, between the theoretical expected value and an estimate of the expected value obtained using empirical information. (You may use the game above as an example.)