Sanderson M. Smith

Home | About Sanderson Smith | Writings and Reflections | Algebra 2 | AP Statistics | Statistics/Finance | Forum

 

GEOMETRIC SETTING EXAMPLE

 

Suppose that your probability of winning a game is 38%, and that each game is independent of any other game. Let x = the number of games played before you win. Then x is a random variable with possible values 1,2,3,4,... . This is a geometric setting with p = .38, and the mean mx = 1/p = 1/.38 = 2.6316.

The probability that x = 1 is 0.38.
The probability that x = 2 is (.62)(.38) = 0.2356.
The probability that x = 3 is (.62)
2(.38) = 0.146072.
etc., etc.

The Excel chart above displays the probability distribution of the random variable x.

The table below shows probability values for x = 1,2,3,...,24,25. The probabilities of getting values greater than 25 are very small. Decimals are shown to four decimal places.

Side note: It is very easy to get these values on your TI-83.
Highlight list L1 and use
seq(x,x,1,25,1).
Highlight list L2 and use
geometpdf(.38,L1).
To get the product column, highlight list L3 and type L1*L2.

The probability and product columns represent rounded figures calculated on a spreadsheet that did the computations using many more decimal places.

x

Probability

(to 4 decimals)

(xi)(pi)

(to 4 decimals)

1

0.3800

0.0038

2

0.2356

0.4712

3

0.1461

0.4382

4

0.0906

0.3623

5

0.0562

0.2808

6

0.0348

0.2089

7

0.0216

0.1511

8

0.0134

0.1071

9

0.0083

0.0747

10

0.0051

0.0514

11

0.0032

0.0351

12

0.0020

0.0237

13

0.0012

0.0159

14

0.0008

0.0106

15

0.0005

0.0071

16

0.0003

0.0047

17

0.0002

0.0031

18

0.0001

0.0020

19

0.0001

0.0013

20

0.0000

0.0009

21

0.0000

0.0006

22

0.0000

0.0004

23

0.0000

0.0002

24

0.0000

0.0002

25

0.0000

0.0001

TOTALS

1.0000

2.6314

This column total is, in reality, just a teensy bit short of 1. Remember that there are an infinite number of x values.

This column total is the mean of the random variable x. Note that this very close to the theoretical mean obtained by using the formula 1/p = 1/.38.

If you have a geometric setting, a simple formula mx = 1/p avoids all of the computation represented in the third column above.

RETURN TO WRITING HOME PAGE

 

 

Home | About Sanderson Smith | Writings and Reflections | Algebra 2 | AP Statistics | Statistics/Finance | Forum

Previous Page | Print This Page

Copyright © 2003-2009 Sanderson Smith