Intervals are independent simultaneous occurrences

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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 Name: Poisson(λ) 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 Parameter: 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, . . . otherwise Statistics: 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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