1
STAT 5112
Spring 2012
Lecture 11
Feb 3, 2012
Jun Xie
3.4 The binomial probability distribution
An experiment that satisfies the following conditions is called a
binomial experiment.
1.
The experiment consists of a sequence of
n
smaller experiments called
trials,
where
n
is fixed in
advance of the experiment.
2.
Each trial can result in one of the same two possible outcomes (dichotomous trials), which we
generically denote by success (
S
) and failure (
F
).
3.
The trials are independent, so that the outcome on any particular trial does not influence the
outcome on any other trial.
4.
The probability of success
P
(
S
) is constant from trial to trial; we denote this probability by
p.
Definition
The
binomial random variable
X
associated with a binomial experiment consisting of
n
trials is defined
as
X
= the number of
S
among the
n
trials
We will often write
X
~ Bin(
n
,
p
) to indicate that
X
is a binomial rv based on
n
trials with success
probability
p.
The pmf of
X
~ Bin(
n
,
p
) is p(x)= =
°
±
²
p
x
(1p)
nx
.
Example 31
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 Fall '08
 BUD
 Binomial, Probability, Probability theory, Binomial distribution, Discrete probability distribution, binomial experiment

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