1 / 9

Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions. Section 5.5: Poisson Distribution. A Poisson distribution is used when the sample size, n, is large and the probability, p, is small and when independent variables occur over time. Poisson Probability Formula.

lesa
Download Presentation

Chapter 5: Discrete Probability Distributions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5: Discrete Probability Distributions Section 5.5: Poisson Distribution

  2. A Poisson distribution is used when the sample size, n, is large and the probability, p, is small and when independent variables occur over time.

  3. Poisson Probability Formula The probability of X occurrences in an interval of time,volume, area, etc., for a variable where: λ (“lambda”) = mean number of occurrences per unit _e-λ∙ λXX! P(X;λ) = *e is a constant like π and is NOT something we will plug a number in

  4. Different ways to find λ: λ = 1) The mean (average) number of occurrences mean is explicitly given to you λ = np (if the probability or percent is given) 2) The number of occurrences in the past (f) total number of outcomes in the past (n) λ = 3)

  5. EXAMPLE 1: A door-to-door salesman averages 2 sales per day.Find the probability of getting 5 sales in a day if thisapproximates a Poisson distribution. 5 (Given) = 2 X =λ = _e-2∙ 255! _e-λ∙ λXX! P(X;λ) = P(5; 2) = = = 0.0361

  6. EXAMPLE 2: probability of 0.2% There is a probability of 0.2% of a defective part in ashipment of computer components. If a shipment of500 components arrives, find the probability of 0 being defective. This approximates a Poisson distrib. 500 components 0 np = 500 (0.002) = 1 X =λ = _e-λ∙ λXX! _e-1∙ 100! P(X;λ) = P(0; 1) = = = 0.3679

  7. EXAMPLE 3: 300 apples were checked for worms and 60 worms were found. What is the probability of an apple withone worm in it if this approximates a Poisson distribution? _# of occurrences_total # of outcomes _60300 1 X = λ = = = 0.2 _e-λ∙ λXX! _e-0.2 ∙ 0.21 1! P(X;λ) = P(1; 0.2) = = = 0.1637

  8. EXAMPLE 4: If there are 200 typographical errors randomly distributed in a 500-page manuscript, find the probability that a given page contains exactly threeerrors. Assume a Poisson distribution. _# of occurrences_total # of outcomes 200500 3 X = λ = = = 0.4 _e-λ∙ λX X! _e-0.4 ∙ 0.43 3! P(X;λ) = P(3; 0.4) = = = 0.0072

  9. p260 #10, 14, 15

More Related