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6.1-11. Suppose that a linear transformation is applied to each of the observations x1 ,x2 ,...

6.1-11. Suppose that a linear transformation is applied to each of the observations x1 ,x2 , . . . , xn in a set of data; that is, a transformed data set y1 , y2 , . . . , yn is created from the original data via the equation yi= axi + b, i = 1, 2, . . . , n, where a and b are real numbers. Show that if xbar and s2X are the sample mean and sample variance of the original data, then the sample mean and sample variance of the transformed data are given by ybar = a xbar + b and s2Y = a2 s2x , respectively.

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