1.5. Some Important Sample Statistics and Their Distributions

We have already encountered two important sample statistics in the previous section, namely the sample mean vector in Equation 1.1 and the sample variance-covariance matrix S in Equation 1.2. These quantities play a pivotal role in defining the test statistics useful in various hypothesis testing problems. The underlying assumption of multivariate normal population is crucial in obtaining the distribution of these test statistics. Therefore, we will assume that the sample y1, ..., yn of size n is obtained from a multivariate population Np(μ, Σ).

As we have already indicated, ~ N

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