16 x to see the rst equality note that if the sum is

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Unformatted text preview: a ﬁnite or countably inﬁnite set of values this is usually done using the probability function. That is, we give P (X = x) for each value of x for which P (X = x) &gt; 0. Example A.8. Binomial distribution. If we perform an experiment n times and on each trial there is a probability p of success, then the number of successes Sn has ✓◆ nk P (Sn = k ) = p (1 p)n k for k = 0, . . . , n k In words, Sn has a binomial distribution with parameters n and p, a phrase we will abbreviate as Sn = binomial(n, p). Example A.9. Geometric distribution. If we repeat an experiment with probability p of success until a success occurs, then the number of trials required, N , has P (N = n) = (1 p)n 1 p for n = 1, 2, . . . In words, N has a geometric distribution with parameter p, a phrase we will abbreviate as N = geometric(p). Example A.10. Poisson distribution. X is said to have a Poisson distribution with parameter &gt; 0, or X = Poisson( ) if P (X = k ) = e k k! for k = 0, 1, 2, . . . To see tha...
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