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The Geometric Distribution also deals with successes and failures. Unlike the Binomial
and Hypergeometric who deal with the number of successes in a certain number of trials,
the Geometric Distribution looks at the time it takes in order to get the first success. Or,
you could interpret X if X is geometric as the number of trials up to and including the 1
st
success.
Pmf of Geometric:
Consider repeated Bernoulli trials with success probability p. Let X denote the number of
trials up to and including the 1
st
success. Then the PMF of the random variable X is:
1
)
1
(
)
(
x
X
p
p
x
p
where x is 1, 2, 3, …
And 0 otherwise.
X is called a geometric r.v. and is said to have the geometric distribution with parameter
p.
Notice that this is the 1
st
time where x can possibly trail off towards infinity. Before we
had x limited by n, the sample size.
If one were to draw a probability histogram of a geometric r.v. what would it look like?
Here is the probability histogram if p=.3. I stopped at x=12. What is the probability of
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 Spring '08
 MARTIN
 Binomial

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