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Learning Objectives
•
Recognize and use the probability mass functions
of common discrete random variables:
–
Uniform
–
Bernoulli
–
Binomial
–
Geometric
–
Poisson
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View Full Document Discrete Uniform
p
X
(
k
)
=
1
b

a
+
1
if
k
=
a
,
a
+
1
,
K
,
b
0 otherw
ise
a
b
1/(ba+1)
Example
p
X
(
k
)
=
1
5

3
+
1
=
0.33 if
k
=
3
,4,5
0 otherw
ise
a = 3
b = 5
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View Full Document Exercises
•
Exercise #141
•
Exercise #142
p
X
(
x
)
=
p
, if
x
=1
1
p
, if
x
=
0
Bernoulli
•
model situations with two outcomes
•
PMF:
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View Full Document Example
•
Tossing a fair coin
•
P(heads) = 0.5
•
P(tails) = 0.5
•
if Heads then X = 1
•
if Tails then X = 0
p
X
(
x
)
=
0.5, if
x
=1
10.5, if
x
=
0
Example
•
A person is either sick or healthy
•
P(disease) = 0.3
•
P(normal) = 0.7
•
if Disease then X = 1
•
if Normal then X = 0
p
X
(
x
)
=
0.3
, if
x
=1
10.3, if
x
=
0
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View Full Document Exercise
•
Exercise #7
Binomial
•
Constructed from a sequence of
n
Bernoulli RV’s with
parameter
p
•
Binomial RV is the number of “successes”
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This note was uploaded on 02/01/2011 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Dunn

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