Question

5 marks) multivariate gaussian probability density is given by: p( x ) = c exp 1 2 b i x i , a i j x i x j where a i j and b i are real constants. Find the expression for the normalization constant c.

Answer 1

3. The Multivariate Normal Distribution

3.1 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.