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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) > 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
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 > 0, or X = Poisson( ) if
P (X = k ) = e k k! for k = 0, 1, 2, . . . To see tha...
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- Spring '10
- The Land