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Examples for 09/08/2011
Fall 2011
Binomial Distribution
:
1.
The number of trials,
n
, is fixed.
2.
Each trial has two possible outcomes:
“success”
and
“failure”.
3.
The probability of “success”,
p
, is the same from trial to trial.
4.
The trials are independent.
5.
X = number of "successes" in
n
independent trials.
Then
( ) ( )
k
n
k
k
n
k
p
p
k
C
n
p
p
k
n
k


⋅
⋅
=


⋅
⋅
=
=
1
1
P
)
(
X
,
where
k
= 0, 1, … ,
n
.
E
(
X
) =
n
⋅
p
Var
(
X
) =
n
⋅
p
⋅
(
1
–
p
)
SD
(
X
) =
( )
p
p
n

⋅
⋅
1
1.
Bart Simpson takes a multiple choice exam in his Statistics 101 class.
The exam has
15 questions, each has 5 possible answers, only one of which is correct.
Bart did not
study for the exam, so he guesses independently on every question.
Let
X
denote the
number of questions that Bart gets right.
a)
Is it appropriate to use Binomial model for this problem?
b)
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