M5L5
Properties of Multiple Random Variables
1.
Introduction
As mentioned in previous lecture, the important measures to explain the properties of
multiple RVs are: moments, covariance, correlation coefficient, conditional mean,
conditional variance, moment generating functions etc. The fundamental properties and
measures those are discussed before for random variables are also applicable for the case of
multiple random variables. Some additional properties and measures are introduced here to
describe the joint variability of two or more components of multiple random variables.
2.
Properties of Multiple Random Variables
The properties are determined by using the concept of expectation. Throughout this lecture,
the following notations will be used:
and
and
3.
Moments of Multiple RVs
The expectation operator or moments introduced in earlier lectures for a single variable can
be extended to two or more variables. Two cases will be discussed in this lecture: discrete
case and continuous case.
3.1.
Discrete Case
In general, the
joint moment of the random variable
and
is given by,
,
and the order of this moment is
. Also
is a second order
moment.
In general we can write:
3.2.
Continuous Case
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Similarly, the
joint moment of the random variable
and
is given by,
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 Spring '13
 Dr.RajibMaity
 Civil Engineering, Variance, Probability theory, Schwarz, Cauchy

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