1 / 17

Hypergeometric & Poisson Distributions

Hypergeometric & Poisson Distributions. Dhon G. Dungca, M.Eng’g. Hypergeometric Distribution. Is the appropriate distribution when sampling without experiment is used in a situation that could qualify as a Bernoulli Process.

gannon
Download Presentation

Hypergeometric & Poisson 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. Hypergeometric & Poisson Distributions Dhon G. Dungca, M.Eng’g.

  2. Hypergeometric Distribution Is the appropriate distribution when sampling without experiment is used in a situation that could qualify as a Bernoulli Process. The probability distribution of the hypergeometric distribution of the hypergeometric variable x is the number of successes in a random sample size n selected from N items of which k are classified as sucesses, and n-k as failures. Its variables are denoted by P(x; N, n, k).

  3. Hypergeometric Distribution The formula for determining the probability of a designated number of successes x is: k N-k h(x; N, n, k) = x n-x N n

  4. Hypergeometric Distribution Where: N – total # of items in population k – number of successes N-k – number of failures n – total # of items in the sample x – number of successes n-x – number of failures

  5. Example 1 If 7 cards are drawn from a deck of playing cards, what is the probability that two will be spades? 0.3357

  6. Example 2 Lots of 40 components each are called unacceptable if they contain as many as 3 defectives or more. The procedure for sampling the lot is to select 5 components at random and to reject a lot if a defective is found. What is the probability that exactly 1 defective is found if there are 3 defectives in the entire lot? 0.3011

  7. Example 3 A homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs. What is the probability that he planted 2 daffodil bulbs and 4 tulip bulbs? 5/14

  8. Example 4 To avoid detection at customs, a traveller has placed 6 narcotic tablets in a bottle containing 9 vitamin pills that are similar in appearance. If a customs official selects 3 tablets at random for analysis, what is the probability that the traveller is arrested for illegal possession of narcotics? 0.8154

  9. Example 5 A company is interested in evaluating its current inspection procedure on shipments of 50 identical items. The procedure is to take a sample of 5 and pass the shipment if no more than 2 are found to be defective. What proportion of 20% defective shipments will be accepted? 0.9517

  10. Poisson Distribution Experiments yielding numerical values of a random variable X, the number of outcomes occurring during a given time interval or in a specified region, are called Poisson Experiments The given time interval may be of any length, such as a minutes, a day, a week, a month or even a year.

  11. Poisson Distribution The probability distribution of the Poisson random variable X, representing the number of outcomes occurring in a given time interval or specified region denoted by t, is: p(x; ) = e - ()x x!

  12. Poisson Distribution Where: e = 2.71828… • = is the average number of successes occurring per stated unit. x = the number of occurrences of the event in the interval of size t.

  13. Example 1 If the number of complaints received daily by the Complaint department of a big department store in Makati is a random variable having a Poisson Distribution mean  = 5, what is the probability that exactly two complaints will be receive on any randomly selected day? 0.0842

  14. Example 2 In a research study, the average train arrival per hour is 1. • What is the probability of exactly 2 arrivals in a given hour? • What is the probability of having 2 or more arrivals in 1 hour? • What is the probability that there will be between 2 and 5 arrivals, inclusive in 1 hour? • What is the probability that there will be 1 arrival between 2pm and 230pm? 0.1839, 0.2642, 0.2636, 0.3033

  15. Example 3 The average quantity demanded for a certain signature item is 5 per day. What is the probability that there will be 20 of these items demanded in a week if a week consists of 6 working days. 0.0134

  16. Example 4 Service calls come to a maintenance center according to a Poisson process and on the average 2.7 calls come per minute. Find the probability that • No more than 4 calls come in any minute • Fewer than 2 calls come in any minute • More than 10 calls come in a 5-minute period 0.8629, 0.24866, 0.7888

  17. Example 5 On the average, a certain intersection results in 3 traffic accidents per month. What is the probability that in any given month at this intersection • Exactly 5 accidents will occur? • Less than 3 accidents will occur? • At least 2 accidents will occur? 0.1008, 0.4232, 0.8009

More Related