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Binomial Random Variables
Binomial Random Variables
Binomial Probability Distributions
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View Full Document Binomial Random
Binomial Random
Variables
Variables
Through 2/25/09 NC State’s freethrow
percentage was 71.4% (384/538; 86
th
in Div.
1).
If in the 2/26/09 game with WFU, NCSU
shoots 11 freethrows, what was the
probability that:
NCSU makes exactly 8 freethrows?
NCSU makes at most 8 free throws?
NCSU makes at least 8 freethrows?
“
“
2outcome” situations are very
2outcome” situations are very
common
common
Heads/tails
Democrat/Republican
Male/Female
Win/Loss
Success/Failure
Defective/Nondefective
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View Full Document Probability Model for this
Probability Model for this
Common Situation
Common Situation
Common characteristics
◦
repeated “trials”
◦
2 outcomes on each trial
Leads to Binomial Experiment
Binomial Experiments
Binomial Experiments
n identical trials
◦
n specified in advance
2 outcomes on each trial
◦
usually referred to as “success” and
“failure”
p
“success” probability;
q=1p
“failure”
probability; remain constant from trial to
trial
trials are independent
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View Full Document Binomial Random Variable
Binomial Random Variable
The
binomial random variable
X
is
the number of “successes” in the
n
trials
Notation:
X has a B(n, p)
distribution, where n is the number
of trials and p is the success
probability on each trial.
Examples
Examples
a.
Yes; n=10; success=“major repairs
within 3 months”; p=.05
b.
No; n not specified in advance
c.
No; p changes
d.
Yes; n=1500; success=“chip is
defective”; p=.10
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View Full Document Binomial Probability
Binomial Probability
Distribution
Distribution
( 29
0
0
trials,
success probability on each trial
probability distribution:
( )
,
0,1,2,
,
( )
( )
( )
(
x
n x
n
x
n
n
n
x
n x
x
x
x
n
p
p x
C p q
x
n
E x
xp x
x
p q
np
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This note was uploaded on 03/10/2011 for the course BUS 350 taught by Professor Reiland during the Spring '08 term at N.C. State.
 Spring '08
 reiland

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