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UCLA
EE131A (KY)
1
EE 131A
Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
M.S. OnLine Engineering Program
Lecture 91
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EE131A (KY)
2
Expectation (averaging) (1)
•
The cdf/pdf
of a rv
X completely characterizes the rv.
Often we may want to have a simpler characterization
of the rv.
The simplest (possibly the most meaningful)
characterization of X is its mean or average.
Ex. 1. Consider the set of numbers {1, 2, 5, 8}.
The
average (as we know from “every day”
experiences) is
= (1 + 2 + 5 + 8) / 4 = 16/4 = 4 .
(1)
•
Let X be a discrete rv
with the sample space
S
= {x
1
,
…, x
n
} and a pmf
of p
i
= P(X = x
i
), i = 1, …, n.
Then
the
expectation
of X (called the
mean
or the
average
)
is defined by
n
ii
i=1
μ
= E X =
x p .
UCLA
EE131A (KY)
3
Expectation (averaging) (2)
Ex. 2.
Consider a Bernoulli rv
X with
S
= {0, 1}, P(X = 1)
= p, and P(X = 0) = q = 1 –
p.
Then the mean is
= 1
p + 0
q = p .
Ex. 3.
Consider a discrete uniform rv
X with
S
= {1, 2, 5,
8}.
That is, P(X = 1) = P(X = 2) = P(X = 5) = P(X = 8)
= ¼
.
Then the mean is
= 1
(¼) + 2
(¼) + 5
(¼) + 8
(¼) = 16/4 = 4 ,
which is the same as in (1) for the deterministic average.
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This note was uploaded on 11/05/2010 for the course ELECTRICAL EE131A taught by Professor Kungyao during the Spring '10 term at UCLA.
 Spring '10
 KungYao
 Electrical Engineering

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