CK-12 Probability and Statistics - Advanced

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

p(x> 2 ) = 1 −p(x≤ 2 )

= 1 −[p( 1 )+p( 2 )]

Before we go any further, we need to findp( 1 )andp( 2 ). Substituting into the formula forp(x):

p( 1 ) = ( 1 −p)^1 −^1 p= (. 5 )^0 (. 5 ) = 0. 5

p( 2 ) = ( 1 −p)^2 −^1 p= (. 5 )^1 (. 5 ) = 0. 25

Then,

p(x> 2 ) = 1 −p(x≤ 2 )

= 1 −(. 5 +. 25 ) = 0. 25

This result says that there is a 25% chance that more than two prospective jurors will be examined before one is
admitted to the jury.

Technology Note

The TI-83/84 calculators have commands for the geometric distribution.

• Press2ndand scroll down (or up) togeometpdf(press[ENTER]to placegeometpdfon your home screen.)
  Type values ofpandxseparated by a comma and press[ENTER]


• Usegeometcdf( for probability ofatleastxsuccesses.

Note:it is not necessary to close the parentheses.

Lesson Summary

1. Characteristics of theGeometric Probability Distribution
   
   
   • The experiment consists of a sequence of independent trials.
   
   
   • Each trial results in one of two outcomes: Success (S) or Failure (F).
   
   
   • The geometric random variablexis defined as the number of trials until the first S is observed.
   
   
   • The probabilityp(x)is the same for each trial.
   
   
   
   


2. Probability distribution, mean, and variance of aGeometric Random Variable

p(x) = ( 1 −p)x−^1 p x= 1 , 2 , 3 ,...

μ=

1

p

σ^2 =

1 −p

p^2

where,

p=Probability of an S outcome

x=The number of trials until the first S is observed