 My Math Forum Poisson distribution and binomial distribution questions

 May 9th, 2009, 09:30 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, 06:49 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 [(1-p)^(n-x)] , 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...riance-of.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) Tags binomial, distribution, poisson, questions ,

,

,

,

,

,

,

,

,

,

,

,

,

,

# questions on bianomial distribution and poision distribution

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post UncleFester Algebra 4 January 19th, 2016 04:27 AM r-soy Probability and Statistics 1 November 16th, 2013 02:09 PM Punch Algebra 6 June 18th, 2012 08:24 PM hoyy1kolko Algebra 2 May 22nd, 2011 02:29 AM jd_jd Advanced Statistics 0 February 11th, 2009 02:26 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      