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May 9th, 2009, 08:30 PM  #1 
Newbie Joined: May 2009 Posts: 4 Thanks: 0  Poisson distribution and binomial distribution questions
Hey i just need to figure out the answers to these questions, not the answers but the method of working, see i dont have a correctr method of working for these questions and i really need them to revise for my upcoming exam. Pl,ease help!!! Thanks in advance! 1. (a) Write down the binomial distribution for x successes in n independent trials each with probability p of success. (b) Write down the Poisson distribution with mean ?. (c) What is the relation between the Poisson distribution and the binomial distribution? (d) A factory produces identical items. On average, 0.2% of the items are known to be defective. If a random sample of 500 items is inspected, what is the probability of there being no more than 3 defective items? 2. (a) Define the Poisson probability distribution with mean ?. (b) Write down the binomial distribution for x successes in n independent trials each with probability p of success. (c) On average, 0.15% of the nails manufactured at a factory are known to be defective. If a random sample of 400 nails is inspected, what is the probability of there being no more than 3 defective nails? 3. (a) Define the Poisson probability distribution with mean p. (b) A tool hire shop has six lawn mowers which it hires out on a daily basis.The number of lawn mowers requested per day follows a Poisson probability distribution with mean 4.5. Find the probability that: (i) exactly three lawn mowers are hired out on any one day; (ii) all lawn mowers are in use on any one day. 
May 11th, 2009, 05:49 AM  #2 
Newbie Joined: Oct 2007 From: india Posts: 9 Thanks: 0  Re: Poisson distribution and binomial distribution questions
binomial distribution is P(x) = C(n,x) p^x [(1p)^(nx)] , x = 0,1,2, ...n poisson distribution is P(x) = e^(?) (?^x) / (x!) , x = 0,1,2, .... see the following page for the pdf http://keral2008.blogspot.com/2008/1...rianceof.html http://rbmix.com/problem/math/poisson/poisson.html If X follows B(n,p) and if n is large and p is small with ? =np (finite), you can assume that X follows Poisson distribution with mean ?. As far as the last part of the first question is concerned if X is the number of defectives out of 500 and you assume binomial with n=500 , p = 0.002 ( from 0.2%) or you can assume poisson approximation with ? =np = 500*0.002 =1 substitute into the poisson pdf and evaluate P(X <=3) = P(X=0)+P(X=1)+P(X=2)+P(X=3) 2(c) is similar in 3(b) mean =4.5 implies ? =4.5 you are asked to find P(X=3) in part(i) 

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