1. (8 points) Let gy, ...y, R be data where n N. Let y = (1) >0 y; and Sy, = 31" (y; y)% (a) (2 points) Show 1" | (y; y) =0 and S, = >0, y? ny*. (b) (4 points) Let n =2 and M N. i. (2 points) Construct a sct of data y;,y that has y = 0 and S5, = M ii. (2 points) Construct a sct of data y,y. that has y = M and S, =0 (c) (2 points) Food in Canada is sold in kilograms and in the US is sold in pounds. One US pound is cqual to 0.454 kilograms. Let yy,..., 1y, represent the amount of food in kilograms from n purchases for a typical shopper, and let zy, ...z, represent these same purchases measured in pounds. i. (1 point) Write z; in terms of y; and write y; in terms of z;. ii. (0.5 points) Supposc y = 32, find z. iii. (0.5 points) Suppose S.. = 20, find Sy