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The Poisson Probability Distribution

The Poisson Probability Distribution. Section 5.8. The Poisson Probability Distribution. Conditions to apply the Poisson Probability Distribution. x is a discrete random variable. The occurrences are random. The occurrences are independent. The average (mean) # of occurrences is known.

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The Poisson Probability Distribution

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  1. The Poisson Probability Distribution Section 5.8

  2. The Poisson Probability Distribution • Conditions to apply the Poisson Probability Distribution. • x is a discrete random variable. • The occurrences are random. • The occurrences are independent. • The average (mean) # of occurrences is known. • Notation of average occurrences is Greek letter lambda. • Lambda is the Poisson Parameter.

  3. Examples • # of telemarketing calls received in a day. • # of defective items in a box of 100. • # of defects in a 5-foot iron rod. • # of accidents on a highway in one week. • # of customers entering a store in a one hour period. • # of tv’s sold at a store during a week.

  4. Poisson Probability Distribution Formula • Used to find the probability of x occurrences during an interval, given the average occurrences during that interval is lambda. (Intervals must be same unit) • P(X) = • ℮ is approximately 2.71828

  5. Example: • An average household receives 9.5 telemarketing calls per week. • Find P(a random household receives 6 calls in a week).

  6. Poisson Probabilities Table: • Appendix C • Calculator • Example: On average 2 new accounts are opened each day at a bank. • Find P(exactly 6 are opened) at this bank on a given day. • Find P(at most 3 are opened) at this bank on a given day.

  7. Poisson Probabilities Table:

  8. Poisson Probability Distribution Table and Graph

  9. Mean and Standard Deviation for a Poisson Distribution µ = lambda σ2 = lambda σ = √ lambda

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