M5L23 - M5L5 Properties of Multiple Random Variables 1...

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    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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M5L23 - M5L5 Properties of Multiple Random Variables 1...

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