Statistical Sciences 2141A/B Lecture Notes - Lecture 16: Poisson Distribution, Random Variable
13 Nov 2018
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Another random variable of interest is the number of events that occur within certain specified boundaries (e. g. , number of defects in an item, number of phone calls received by an operator within a certain time limit) A poisson random variable x is an rv associated with modeling the number of times that a certain event occurs per unit of time, distance or volume. We de(cid:374)ote that x is a poisso(cid:374) r(cid:448) (cid:271)y x ~ p(cid:894) (cid:895) (cid:449)here > 0. Suppose the (cid:374)u(cid:373)(cid:271)er of errors i(cid:374) a pie(cid:272)e of soft(cid:449)are has a poisso(cid:374) distri(cid:271)utio(cid:374) (cid:449)ith = (cid:1007) (cid:894)(cid:449)hi(cid:272)h immediately implies that the expected number or errors is 3 and the variance is also 3). Lecture notes page 1 approaches the p(cid:373)f for p(cid:894) (cid:895) If for x ~ b(n, p) we let n and p 0 i(cid:374) such a way that (cid:374)p > 0, the(cid:374) the pmf for b(n, p)
