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Unformatted text preview: peatedly over a period of time
Occurrences in disjoint time intervals are independent
Simultaneous occurrences are very rare
The average number of occurrences per unit time is constant
throughout the time period Math 30530 (Fall 2012) Discrete Random Variables October 7, 2012 9 / 10 The Poisson random variable
When to use: When you are counting the number of occurrences
of an event in unit time, when the occurrences satisfy the
conditions of the Poisson process; or, when you are approximating
X ∼ Binomial(n, p) with n large, p small, np moderate
λ: the average number of occurrences per unit time, or np Mass function:
pX (x ) = λx − λ
x! e 0 if x = 0, 1, 2, 3, . . .
µ = E (X ) = λ
σ 2 = Var(X ) = λ Math 30530 (Fall 2012) Discrete Random Variables October 7, 2012 10 / 10...
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- Spring '11