EBook Problems Limits LLN

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EBook Problems Set - Law of Large Numbers

Problem 1

Your friend is in Vegas playing Keno, and he has noticed that some numbers have been coming up more frequently than others. He declares that the other numbers were "due" to come up, and puts all of his money on those numbers. Is this a correct assessment?

• Choose one answer.
(a) Yes, the Law of Averages says that the numbers that haven't shown up will now come up more often, because the probabilities will even out in the end.
(b) No, this is a misconception, because random phenomena do not "compensate" for what happened in the past.
(c) No, the game is probably broken, and the other numbers won't be coming up more frequently.
(d) Yes, the more often a certain number doesn't come up, its probability of coming up next turn increases.

Problem 2

You are flipping a coin, and it has already landed heads seven times in a row. For the next flip, the probability of getting tails will be greater than the probability of getting heads.

• Choose one answer.
(a) TRUE
(b) FALSE