Let x₁,x₂,...,x_n be a sample of data and let c be a non-zero constant.

Should include R and/or Excel code and functions.

Problem 1) Let X1, X2, ..., Xn be a sample data and let c be a non-zero constant. a) Suppose y; = x; +c, i = 1, 2, ..., n. Prove that y = 1 +c, and that sy = Sx, where sy, and Sy are the standard deviations of y and x respectively. b) Suppose y; = cxi, i = 1, 2, ..., n. Prove that 5 = c, and that sy = 1c| sx Problem 1) Let X1, X2, ..., Xn be a sample data and let c be a non-zero constant. a) Suppose y; = x; +c, i = 1, 2, ..., n. Prove that y = 1 +c, and that sy = Sx, where sy, and Sy are the standard deviations of y and x respectively. b) Suppose y; = cxi, i = 1, 2, ..., n. Prove that 5 = c, and that sy = 1c| sx