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.
|
|
|
|
0.3800 |
0.0038 |
|
0.2356 |
0.4712 |
|
0.1461 |
0.4382 |
|
0.0906 |
0.3623 |
|
0.0562 |
0.2808 |
|
0.0348 |
0.2089 |
|
0.0216 |
0.1511 |
|
0.0134 |
0.1071 |
|
0.0083 |
0.0747 |
|
0.0051 |
0.0514 |
|
0.0032 |
0.0351 |
|
0.0020 |
0.0237 |
|
0.0012 |
0.0159 |
|
0.0008 |
0.0106 |
|
0.0005 |
0.0071 |
|
0.0003 |
0.0047 |
|
0.0002 |
0.0031 |
|
0.0001 |
0.0020 |
|
0.0001 |
0.0013 |
|
0.0000 |
0.0009 |
|
0.0000 |
0.0006 |
|
0.0000 |
0.0004 |
|
0.0000 |
0.0002 |
|
0.0000 |
0.0002 |
|
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.
Home | About Sanderson Smith | Writings and Reflections | Algebra 2 | AP Statistics | Statistics/Finance | Forum
Previous Page | Print This Page
Copyright © 2003-2009 Sanderson Smith