III More Discrete Probability Distributions B Poisson Distribution
III. More Discrete Probability Distributions B. Poisson Distribution In a binomial experiment you are interested in finding the probability of a specific number of successes in a given number of trials. Suppose instead that you want to know the probability that a specific number of occurrences takes place within a given unit of time or space. For instance, to determine the probability that an employee will take 15 sick days within a year, you can use the Poisson distribution. 1. The Poisson distribution is a discrete probability distribution of a random variable x that satisfies the following conditions: a. The experiment consists of counting the number of times, x, an event occurs in a given interval. The interval can be an interval of time, area, or volume. b. The probability of the event occurring is the same for each interval. c. The number of occurrences in one interval is independent of the number of occurrences in other intervals.
III. More Discrete Probability Distributions B. Poisson Distribution Try it Yourself – Page 224 What is the probability that more than four accidents will occur in any given month at the intersection? By hand, we need to find the probabilities for 1, 2, 3, and 4 accidents and add them up. We then subtract that from 1 to get the probability of more than 4 accidents occurring. P(0) =. 04979; P(1) =. 14936; P(2) =. 22404; P(3) =. 22404; P(4) =. 16803 1 – (. 04979 +. 14936 +. 22404 +. 16803) =. 1847 Using the calculator, we use the Poissoncdf function to find the probability of up to 4 accidents occurring and then subtract that from 1. 2 nd VARS D, 3 and 4 =. 81526 1 -. 81526 =. 1847, the same answer we got doing it by hand.
There is a full page summary chart detailing the different discrete probability distributions and their formulas on page 225 in your book. I strongly recommend spending time looking that over and becoming familiar with the information it contains!!
Assignments: Classwork: Page 226; #1– 8, 11– 16 Homework: Pages 227; #17– 24
- Slides: 9