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3. The Multivariate Normal Distribution

3. The Multivariate Normal Distribution Introduction A generalization of the familiar bell shaped Normal density to several dimensions plays a fundamental role in Multivariate analysis While real data are never exactly Multivariate Normal , the Normal density is often a useful approximation to the true population Distribution because of a central limit effect. One advantage of the Multivariate Normal Distribution stems from the fact that it is mathematically tractable and nice results can be obtained. 1. To summarize, many real-world problems fall naturally within the framework of Normal theory. The importance of the Normal Distribution rests on its dual role as both population model for certain natural phenomena and approximate sampling Distribution for many statistics.

The Multivariate Normal Distribution 3.1 Introduction A generalization of the familiar bell shaped normal density to several ... Example 3.8 (Linear combinations of random vectors) Let X 1;X 2;X 3 and X 4 be independent and identically distributed 3 1 random vectors with = 2 4 3 1 1 3 5 and = 2 4 3 1 1 1 1 0 1 0 2 3 5 (a) nd the mean and ...

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