CS 70 Note 19
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CS 70 Discrete Mathematics and Probability Theory
Spring 2015 Vazirani Note 19
Some Important Distributions
Recall our basic probabilistic experiment of tossing a biased coin n times. This is a very simple model, yet
surprisingly powerful. Many important probability distributions that are widely used to model real-world
phenomena can be derived from looking at this basic coin tossing model.
The rst example, which we have seen in Note 16, is the binomial distribution Bin(n, p). This is the distri-
bution of the number of Heads, Sn , in n tosses of a biased coin with probability p to be Heads. Recall that
the distribution of Sn is Pr[Sn k] n pk (1 p)nk for k {0, 1, . . ....
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