STAT 3201 Lecture Notes - Lecture 12: Poisson Distribution, Binomial Distribution
13 Feb 2017
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Document Summary
Goal: find the probability distribution of the number of automobile accidents at a particular intersection during a time period of one week. Let the time period (one week) be split up into n subintervals, each of which is so small that at most one accident could occur in it with a probability, denoted by p, greater than. Then: p(an accident occurs in a subinterval)=p, p(no accidents occur in a subinterval)=1-p, p(more than one accident occurs in a subinterval)=0. Assume that the occurrence of accidents can be regarded as independent from subinterval to subinterval. Issues: there is no way of creating subintervals, we do not know n, we do not know p, but, as we increase n we know the probability p of an accident occurring in one of the subintervals decreases. The binomial probability function converges to the poisson, which implies that poisson probabilities can be used to approximate binomial probabilities for large n and small p.
