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Binomial Random Variable
Submitted by gfj100 on Wed, 11/11/2009  10:41
This is a specific type of discrete random variable. A binomial random variable counts how often
a particular event occurs in a fixed number or tries. For a variable to be a binomial random
variable, these conditions must be met:
•
There are a fixed number of trials (a fixed sample size).
•
On each trial, the even of interest either occurs or does not.
•
The probability of occurrence (or not) is the same on each trial.
•
Trials are independent of one another.
Examples of binomial random variables:
•
Number of correct guesses at 30 truefalse questions when you randomly guess all
answers
•
Number of winning lottery tickets when you buy 10 tickets of the same kind
•
Number of lefthanders in a randomly selected sample of 100 unrelated people
Notation
n
= number of trials (sample size)
p
= probability event of interest occurs on any one trial
Example
: For the guessing at true questions example above, n = 30 and p = .5 (chance of
getting any one question right).
Probabilities for binomial random variables
The conditions for being a binomial variable lead to a somewhat complicated formula for finding
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 Spring '11
 AndyRegards
 Binomial

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