THE GEOMETRIC SETTING

Sanderson M. Smith

THE GEOMETRIC SETTING

(MINI-PROJECT BY BRAD)

Brad's poster provides an explanation of the geometric setting along with an example.

The geometric setting:

Each observation falls into one of two categories: Success or Failure (or whatever you wish to call them).
The probability of success is the same for each observation.
The observations are independent.
The variable of interest is the number of trials required to obtain the first success.

Brad's graphics display relates to the random variable x, where x is the number of times a single die must be rolled until a 6 occurs. Possible values for x are 1,2,3,4,......

Here are some of the probabilities displayed in Brad's chart.

Value of x	Probability
1	1/6 = 16.67%
2	(5/6)(1/6) = 13.89%
3	(5/6)²(1/6) = 11.57%
4	(5/6)³(1/6) = 9.65%
5	(5/6)⁴(1/6) = 8.04%
6	(5/6)⁵(1/6) = 6.70%
7	(5/6)⁶(1/6) = 5.58%
8	(5/6)⁷(1/6) = 4.65%
9	(5/6)⁸(1/6) = 3.88%
10	(5/6)⁹(1/6) = 3.23%
11	(5/6)¹⁰(1/6) = 2.69%
12	(5/6)¹¹(1/6) = 2.24%
13	(5/6)¹²(1/6) = 1.87%
14	(5/6)¹³(1/6) = 1.56%
15	(5/6)¹⁴(1/6) = 1.30%
16	(5/6)¹⁵(1/6) = 1.08%
17	(5/6)¹⁶(1/6) = 0.90%
18	(5/6)¹⁷(1/6) = 0.75%
19	(5/6)¹⁸(1/6) = 0.63%
20	(5/6)¹⁹(1/6) = 0.52%

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