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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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III.71. Probability Distributions

James Norris

1 Discrete Distributions

When we toss a coin, we have no idea whether it will land heads or tails. However, there is a different sense in which the behavior of the coin is highly predictable: if it is tossed many times, then the proportion of heads is very likely to be close to Image.

In order to study this phenomenon mathematically, we need to model it, and this is done by defining a sample space, which represents the set of possible outcomes, and a probability distribution on that space, which tells you their probabilities. In the case of a coin, the natural sample space is the set {H, T}, and the obvious ...

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