elemprob-page13 - so E X 2 = E ( X 2- X ) + | EX = 2 + ,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: so E X 2 = E ( X 2- X ) + | EX = 2 + , and hence Var X = . Example. Suppose on average there are 5 homicides per month in a given city. What is the probability there will be at most 1 in a certain month? Answer. If X is the number of homicides, we are given that E X = 5. Since the expectation for a Poisson is , then = 5. Therefore P ( X = 0) + P ( X = 1) = e- 5 + 5 e- 5 . Example. Suppose on average there is one large earthquake per year in California. Whats the probability that next year there will be exactly 2 large earthquakes? Answer. = E X = 1, so P ( X = 2) = e- 1 ( 1 2 ). We have the following proposition. Proposition 5.1. If X n is binomial with parameters n and p n and np n , then P ( X n = i ) P ( Y = i ) , where Y is Poisson with parameter . The above proposition shows that the Poisson distribution models binomials when the probability of a success is small. The number of misprints on a page, the number of automobile accidents, the number ofa success is small....
View Full Document

Ask a homework question - tutors are online