STAT 205 Probability Theory Fall 2006

نویسنده

  • Hang Bai
چکیده

Let λ ≥ 0 and n ∈ N \ {0} and consider the partition of (0,∞) into the halfopen intervals I1, I2, . . . where Ii = ((i − 1)/n, i/n]. Take a sequence X1, X2, · · · of independent random variables with Xi ∼ Bernoulli(λ/n), i.e., P (Xi = 1) = λ/n and P (Xi = 0) = 1− λ/n. We can interpret Xi = 1 to mean that a certain event was observed in the time period Ii. As n becomes large these time periods become small, and so does the probability of observing an event in any particular one of them, but the expected number of observed events per unit time remains λ.

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تاریخ انتشار 2011