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Chapter 8: Discrete Probability Distributions
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Figure 8-17:
Display of the design for a Geometric Experiment
Next we will present the definition of a geometric experiment.
Definition: Geometric Experiment
A Geometric experiment is a random experiment in which the sequence of
Bernoulli trials are independent, there is two possible outcomes on each trial,
the probability of a success is fixed from trial to trial, and we are interested
in the occurrence of the first success in the sequence.
The function which generates the probability of observing the first success in
trials in a geometric experiment is given next.
Example 8-17
: The defective rate for a manufacturing process is 1%. If
items are selected at random and examined, what is the probability that the
first defective item found is the sixth item which is examined?
Solution:
The experimental design of observing the first defective
(success) on the 6
th
trial is displayed in
Figure 8-18
.