First we provide a simple derivation of the density of a chi-square random variable. Then we provide another simple proof of the statistical independence of the sample mean and the sample variance of a random sample from a normal distribution. The technique proving independence readily extends to the multivariate case.

TR Number: 
2007-02
Gauri Sankar Datta
Key Words: 
Chi-square distribution; Moment generating function; Wishart distribution.

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