1 / 10

STATISTIC & INFORMATION THEORY (CSNB134)

This module explores the Poisson distribution, a key concept in random variable statistics. We will cover the characteristics of the Poisson random variable, which models the number of occurrences of an event in a given time or space. Examples include traffic accidents and machine breakdowns. We will also address probability calculations, using cumulative probability tables and relevant exercises to illustrate the concept. By the end of this module, you will have a solid grasp of the Poisson distribution and its applications in real-world scenarios.

jonah-duke
Télécharger la présentation

STATISTIC & INFORMATION THEORY (CSNB134)

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. STATISTIC & INFORMATION THEORY (CSNB134) MODULE 7B PROBABILITY DISTRIBUTIONS FOR RANDOM VARIABLES ( POISSON DISTRIBUTION)

  2. Overview • In Module 7, we will learn three types of distributions for random variables, which are: - Binomial distribution - Module 7A - Poisson distribution - Module 7B - Normal distribution - Module 7C • This is a Sub-Module 7B, which includes lecture slides on Poisson Distribution.

  3. The Poisson Random Variable • The Poisson random variable xis a model for data that represent the number of occurrences of a specified event in a given unit of time or space. • Examples: • The number of calls received by a switchboard during a given period of time. • The number of machine breakdowns in a day • The number of traffic accidents at a given intersection during a given time period.

  4. For values of k = 0, 1, 2, … The mean and standard deviation of the Poisson random variable are Mean: m Standard deviation: The Poisson Probability Distribution • x is the number of events that occur in a period of time or space during which an average of m such events can be expected to occur. The probability of k occurrences of this event is

  5. Exercise 1 The average number of traffic accidents on a certain section of highway is two per week. Find the probability of exactly one accident during a one-week period.

  6. Cumulative Probability Tables • You can use the cumulative probability tables to find probabilities for selected Poisson distributions. • Find the column for the correct value of m. • The row marked “k” gives the cumulative probability, P(x  k) = P(x = 0) +…+ P(x = k)

  7. Exercise 2 (Similar case of Exercise 1). What is the probability that there is exactly 1 accident? • Find the column for the correct value of m.

  8. Exercise 2 (cont.) (Similar case of Exercise 1).What is the probability that there is exactly 1 accident? P(x = 1) = P(x 1) – P(x  0) = .406 - .135 = .271 Check from formula: P(x = 1) = .2707

  9. Exercise 2 (cont.) What is the probability that 8 or more accidents happen? Is it common for an accident to happen 8 or more times in a week? P(x 8) = 1 - P(x< 8) = 1 – P(x  7) = 1 - .999 = .001 This would be very unusual (small probability) since x = 8 lies standard deviations above the mean.

  10. STATISTIC & INFORMATION THEORY (CSNB134) PROBABILITY DISTRIBUTIONS OF RANDOM VARIABLES (POISSON DISTRIBUTIONS) --END--

More Related