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ECMT 1020
Summer School 09
Lecture 8 Random
Variables and Portfolio
Analysis
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View Full Document Experiment:
Toss 2 Coins.
Let
X = # heads.
T
T
Discrete Probability
Distribution
4 possible outcomes
T
T
H
H
H
H
Probability Distribution
0
1
2
X
X Value
Probability
0
1/4 = 0.25
1
2/4 = 0.50
2
1/4 = 0.25
0.50
0.25
Probability
Discrete Random Variable
Summary Measures
•
Expected Value (or mean)
of a discrete
distribution
(Weighted Average)
•
Example:
Toss 2 coins,
X
= # of heads
,
compute expected value of X:
E(X) = (0 x 0.25) + (1 x 0.50) + (2 x 0.25)
= 1.0
X
P(X)
0
0.25
1
0.50
2
0.25
∑
=
=
=
μ
N
1
i
i
i
)
X
(
P
X
E(X)
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View Full Document •
Variance
of a discrete random variable
•
Standard Deviation
of a discrete random
variable
where:
E(X) = Expected value of the discrete random variable X
X
i
= the i
th
outcome of X
P(X
i
) = Probability of the i
th
occurrence of X
Discrete Random Variable
Summary Measures
∑
=

=
N
1
i
i
2
i
2
)
P(X
E(X)]
[X
σ
(continued)
∑
=

=
=
N
1
i
i
2
i
2
)
P(X
E(X)]
[X
σ
σ
–
Example:
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This note was uploaded on 02/10/2012 for the course ECON 1002 taught by Professor Markmelatos during the Three '10 term at University of Sydney.
 Three '10
 MarkMelatos
 Macroeconomics

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