Let A1, A2,...,A, represent n mutually independent normal variables with means /, #2,..., H. . and variances or , 62,..., , respectively. i) If Y = [c;X; , where c1, C2,...,,, are real constant, find the distribution of Y. i=1 (n -1)$2 ii) If x ~ N(u, o' ) and W = ~ x'(n-1), show that distribution of Q = X - H 02 s/ vn follow t - distribution and state its degree of freedom