18. A computationally efficient way to compute the sample mean and sample variance of the data set x1, x2, . . . , xn is as follows. Let

be the sample mean of the first j data values; and let

be the sample variance of the first j, j ≥ 2, values. Then, with s2 1 =0, it can be shown that

(a) Use the preceding formulas to compute the sample mean and sample variance of the data values 3, 4, 7, 2, 9, 6.

(b) Verify your results in part

(a) by computing as usual.

(c) Verify the formula given above for ¯xj+1 in terms of ¯xj .

x= xj j=1,...,n