13. Consider a sample x1, . . . , xn from some statistical population, and let x, S2x

, and Sx denote the sample mean, sample variance, and sample standard deviation.

(a) Suppose that the xi values are coded to y1, . . . , yn, where yi = c1+xi, where c1 is a known constant. Show that the sample mean, sample variance, and sample standard deviation of y1, . . . , yn are y = c1 + x, S2y

= S2x

, Sy = Sx.

(b) Suppose that the xi values are coded to y1, . . . , yn, where yi = c2xi, where c2 is a known constant. Show that the sample mean, sample variance, and sample standard deviation of y1, . . . , yn are y = c2x, S2y

= c22 S2x

, Sy = |c2|Sx.

(c) Suppose that the xi values are coded to y1, . . . , yn, where yi = c1+c2xi, where c1, c2 are known constants.

Show that the sample mean, sample variance, and sample standard deviation of the statistical population y1, . . . , yn are y = c1 + c2x, S2y

= c22 S2x

, Sy = |c2|Sx.