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 ...
Given a population of N units, it is required to draw a random sample of n distinct units in such a way that the probability for the ith unit to be in the sample is proportional to its "size" xi ...