Poisson Distribution s Definition The Poisson Distribution occurs
Poisson Distribution s
Definition The Poisson Distribution occurs when: There are discrete events in a continuous interval of space or time. Eg Phone calls per hour, Earthquakes per year, Potholes per km. (a) Trials are independent. (b) The events cannot occur simultaneously (c) Events are random and unpredictable (d) The probability of an event occurring is proportional to the interval length (for small intervals)
Examples when the Poisson distribution arises (a) The number of phone call arriving at an exchange in an hour. (b) Typing errors on a page of an author’s manuscript. (c) The number of faults on a computer’s circuitry over the period of a month. (d) The number of organisms present in 1 litre of milk.
Poisson Formula If X represents the number of successes then: PARAMETERS of Poisson distribution (what describes the distribution) λ = mean number of occurrences per interval
E(x) and Standard Deviation E(x) = λ = Var(x)
Examples Example 1 The average number of emergency calls that a hospital gets on any day is 4. What is the probability that the hospital gets 6 calls on a particular day?
Examples Example 2 What is the probability that the hospital gets less than 4 calls on a particular day?
Adjusting λ Example 3 During weekdays a garage knows that on average 10 cars per hour are served. What is the probability that during a particular 15 minute interval, there will be some cars wanting service?
Adjusting λ Example 4 On average 1 get 6 emails per hour. What is the probability that during a particular 15 minute interval, there will be less than 3 emails received?
Practice: 0 H/W Book: Page 190 and 191 0 Text Book Page 239 Question 4 parts a) and b).
- Slides: 10