02_16 - h) What is the probability that there will be...

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STAT 400 Examples for 02/16/2011 Spring 2011 Poisson Distribution : X = the number of occurrences of a particular event in an interval of time or space. P( X = x ) = ! λ λ x x e - , x = 0, 1, 2, 3, … . E( X ) = λ , Var( X ) = λ . Table III ( pp. 580 – 582 ) gives P( X x ) EXCEL: = POISSON( x , λ , 0 ) gives P( X = x ) = POISSON( x , λ , 1 ) gives P( X x ) 1. Traffic accidents at a particular intersection follow Poisson distribution with an average rate of 1.4 per week. a) What is the probability that the next week is accident-free? b) What is the probability that there will be exactly 3 accidents next week? c) What is the probability that there will be at most 2 accidents next week?
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d) What is the probability that there will be at least 2 accidents during the next two weeks? e) What is the probability that there will be exactly 5 accidents during the next four weeks? f) What is the probability that there will be 2 accidents tomorrow? g) What is the probability that the next accident will not occur for three days?
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Unformatted text preview: h) What is the probability that there will be exactly two accident-free weeks during the next four weeks? When n is large ( n 20 ) and p is small ( p 0.05 ) and n p 5, Binomial probabilities can be approximated by Poisson probabilities. For this, set = n p . 2. Suppose the defective rate at a particular factory is 1%. Suppose 50 parts were selected from the daily output of parts. Let X denote the number of defective parts in the sample. a) Find the probability that the sample contains exactly 2 defective parts. b) Use Poisson approximation to find the probability that the sample contains exactly 2 defective parts. c) Find the probability that the sample contains at most 1 defective part. d) Use Poisson approximation to find the probability that the sample contains at most 1defective part....
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This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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02_16 - h) What is the probability that there will be...

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