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Unformatted text preview: Lecture 13. Continuous Distributions In a continuous probability space, the probabilities of events cannot be derived from the probabilities of the individual outcomes in them. In many cases, events containing only finitely many outcomes have zero probability. Example. What does it mean to pick a point at random from the unit interval, if no point is to be any more probable than any other? If the interval is divided half, then we must grant that the random point must have equal probability of being in either half, and hence the probability of being in the first half must be 1 / 2, and the probability of being in the second must be the same. Similarly, if the interval is divided into thirds, the probability of being in the first third must be the same as the probability of being in the second and the same as being in the third, and hence the probability of being in any given third must be 1 / 3. In the same manner, if the interval is divided into n subsets each of the same length, then the probability o being in any selected one of the equal parts must be 1...
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 Spring '08
 Britt
 Probability

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