CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 4. Discrete Probability Distribution

This is of course an infinite sum and it is impossible to compute. However, we can use the complementation rule,

p(x≥ 2 ) = 1 −p(x≤ 1 )

= 1 −[p( 0 )+p( 1 )]

—Calculating,—

= 1 −

( 2. 5 )^0 e−^2.^5

0!

−

( 2. 5 )^1 e−^2.^5

1!

≈ 0. 713

So, according to the Poisson model, the probability that two or more sightings are made in a month is 71.3%

Technology Note

The TI-83/84 calculators and the EXCEL spreadsheet have commands for the Poisson distribution.

UsingtheTI-83/84Calculators

• Press[DIST]and scroll down (or up) topoissonpdf( Press[ENTER]to placepoissonpdfon your home
  screen.) Type values ofμandxseparated by commas and press[ENTER].


• Usepoissoncdf(for probability ofatmostxsuccesses.

Note:it is not necessary to close the parentheses.

UsingEXCEL

• In a cell, enter the function =poisson(μ,x, false), whereμandxare numbers. Press[Enter]and the probability
  ofxsuccesses will appear in the cell.


• For probability ofatleastxsuccesses, replace “false” with “true”

Lesson Summary

1. Characteristics of thePoisson Distribution:
   
   
   • The experiment consists of counting the number of events that will occur during a specific interval of time or
     in a specific distance, area, or volume.
   
   
   • The probability that an event occurs in a given time, distance, area, or volume is the same.
   
   
   • Each event is independent of all other events.
   
   
   
   

2.Poisson Random Variable

Mean and Variance