## ABSTRACT

This chapter discusses multivariate normal distribution's properties in some detail since the estimation of its parameters is the source of many standard multivariate statistical methods. The term 'linear compound' is used to refer to a transformation applied to a vector random variable to produce a new random variable. The term 'linear combination' is used to refer to a weighted sum of vector random variables which is itself a vector random variable, and it will be applied in later sections to linear combinations of the vector responses of different individuals. The Wishart distribution is the multivariate generalization of the χ^{2} distribution. χ^{2}(f) may be defined as the distribution of the sum of squares of f independent standard normal variates. The chapter defines the Wishart distribution in a similar way and derives some of its properties. It then discusses Hotelling T^{2}-distribution. The distribution is named after Harold Hotelling, who proposed it as a multivariate generalization of the Student t-distribution.