Example 1: The population from which samples are selected is {1,2,3,4,5,6}. This population has a mean of 3.5 and a standard deviation of 1.70783. The next display shows a histogram of the population.

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A sample (X1,⋯ ,Xn) is drawn from a population of size N. Karlin (1974) conjectured that for any function Φ in a certain class of real-valued functions on the sample space, Eφ (X1,⋯ ,Xn) is at least ...

Mathematical Proceedings of the Royal Irish Academy, Vol. 99A, No. 2 (Dec., 1999), pp. 171-177 (7 pages) In this paper we derive the exact covariance of some sample moments for 'simple random sampling ...