Abstract. First four initial moments of the sample variance are derived. The four central moments of the sample mean are represented, and values are checked via characteristic functions. Obtained results are verified for a normal population. We numerically obtain probability density functions of the sample variance of random variables exponentially distributed via Pearson family. In discrete case, for Bernoulli distributed random variables, some example concerning probability mass functions are presented. Graphical representation and comparison with standard approximation are performed.

Received: May 12, 2012

AMS Subject Classification: 62H10, 60E05, 62E17

Key Words and Phrases: sample mean, sample variance, moments, Pearson system

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