By Max Jammer
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4. (*, - ^i) (x, - /i) J=i+1 61 ESTIMATION 4. (c) Derivation of the minimum variance linear estimator of the popula tion mean assuming independence between sample values. a2 + 2 CONTINUOUS PROBABILITY DISTRIBUTIONS 27 is usually denoted by p(x)dx and it is represented by the shaded strip labelled (1) in Fig. 1. 5) that the probability that x0 takes a value within the range x to x + 2dx is the sum of the probability that x0 takes a value within the range x to x -f dx and the probability that x0 takes a value within the range x + dx to x + 2dx since these two intervals are mutually exclusive. 1) x x+dx FIG. 1. The normal distribution. may be summed (or, rather, integrated) to yield the probability that x0 takes a value in a non-infinitesimal interval Xj to x2. The second possibility is to develop, either from theoretical considerations or by inference from the sample, an alternative mathematical form for the population distribution and to use this to describe the population. There are two systems of distributions available which provide a wide range of distribution forms and means of obtaining the values of parameters required to fit a distribution. These are the Pearson system described in Elderton (1935) and the Johnson system described in Johnson (1947).