The University of Hong Kong
Department of Statistics and Actuarial Science
STAT1301 Probability and Statistics I
Example class 9 Expected Values
I.
The
Expected Value
of a Random Variable
(a) If X is a discrete random variable with frequency function p(x), the expected value of
X, denoted by E(X), is
(b)
If X is a continuous random variable with density f(x), then
E(X) is also referred to as the mean of X and is often denoted by
μ
.
II.
Variance
and
Standard Deviation
The standard deviation is an indication of how dispersed the probability distribution is
about its center, or about its expectation.
(a) If X is discrete random variable with frequency function p(x) and expected value
μ
=E(X),
(b) If X is continuous random variable with density function f(x) and E(X) =
μ
.
Theorem A
III.
Linear Combinations of Random Variables
i.
ii.
Exercise
1.
Suppose E(X) = expected value of X, prove the Theorem
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 Spring '08
 SMSLee
 Statistics, Probability, Variance, Probability theory, probability density function, new employee

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