Sampling theory is a study of the relationship existing between a population and samples drawn from the population. It is useful in estimating unknown population parameters such as population mean and variance from knowledge of corresponding sample mean and variance, often called *sample statistics*. Sampling theory is also useful in determining whether the observed differences between two samples are due to chance variation or they are really significant. Such questions arise for testing differences in returns among assets. For instance, is the difference between returns on S&P 500 and the Nikkei 225 significant? Likewise, is the volatility of one index different from the volatility of another index? The analysis of differences in samples involves the formulation of hypotheses and applications of tests of significance that are important in the theory of decisions. In order for the conclusions of sampling theory and statistical inference to be valid, samples must be chosen so as to be representative of the population. One way in which a representative sample may be obtained is by the process called *random sampling*, according to which each member of a population has an equal chance of being included in the sample.

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