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SAMPLE STATISTICS
sample points. Examples are the sample mean ¯x = x i/n and the sample variance s2 = (x i − ¯x)2/n A random sample may be regarded as a microcosm of the population from which it is drawn. Therefore, we might attempt to estimate the moments of the population’s p.d.f f(x) by the corresponding moments of the sample statistics.
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consistent. Observe that Themean ¯ x V ,x x i x
www.le.ac.ukA random sample x 1,x 2 ... variate are E (u)= n and V (u)=2 n respectively. Theorem. The sum of two independent chi-square variates is a chi-square variate with degrees of freedom equal to the sum of the degrees of freedom of its additive components. If x
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