Pretend that Barry Bonds has just hit his 61 ^st home run of the season. Assume that he hits a home run with probability 0.125 each time he bats, and that this event is independent between at-bats (we know that this is not exactly the case, but pretend it is).

1. (5) If he has 80 total at-bats remaining, what is the distribution of Y = the number of additional home runs he hits? Specify it completely.
2. (5) What is the expected value of Y ? (this would be your best point-prediction for the number of additional home runs he hits).
3. (5) What is the probability that he hits at least 9 additional home runs in these 80 at-bats?
4. (5) What is the probability that he hits exactly 9 additional home runs in these 80 at-bats?

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