Problem 1. Linear Transformations Suppose we are given a data set {031, (12, . . . , dn} and know its mean, variance, and standard deviation to be meand, 11am, and stdd. Consider another data set {t1,t2, . . . ,tn}, Where t, is a linear transformation of d,: ti=f(d)=a'di+b for each 2' = 1,2,... ,n. Here, a and b are arbitrary constants. Let meant, van, and std, be the mean, variance, and standard deviation of the transformed data. a) (36 Express mean, in terms of meand, a, and b. b) [38 Express van in terms of mm, a, and b. c) 6' Express std, in terms of stdd, a, and b