6. Let Z = (Z1, . .., Za) have i.i.d. components Zj ~ N(0, 1), j = 1, ..., d. (a) Compute the joint ChF of the vector Z. Explain. (b) For a (d x m)-matrix A and a (row) vector a = (al, . .., am) E Rm, derive the joint ChF of X := a + ZA. (c) Assuming that m = d and the matrix A is orthogonal, compute the covariance matrix of X and hence derive the distribution of ||X - all? = _1(Xj - a;)2. Hints: (a) The ChF of N(0, 1) is given at the end of the paper. [2+ 4+5 =11]