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

j=1,...,n be the sample mean of the first j data values, and let (x-x1) j-1 j=2,...,n be the sample variance of the first j, j 2, values. Then, with s = 0, it can be shown that Xj+1-xj j+1 and $+1 = (1 } }) s + (j + 1)(x;+1 x;) a. Use the preceding formulas to compute the sample mean and sam- ple 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 x;+ in terms of x;.