13. (i) Let XI" ' " Xn be a sample from N( t ( 2 ), and consider the problem of deciding between Wo: < 0 and WI : O. If x = Ex;/n and C = (a l /ao) 2/n, the likelihood-ratio procedure takes decision do or dl as 1.10] {nx < k or > k , VE( x, - X)2 where k = - if C> 1 and k = ";(1 - C)/C if C < 1. (ii) For the problem of deciding between wo : 0 < 00 and WI : 0 00, the likelihood ratio procedure takes decision do or

d, as E(x; - X)2 nol < or > k , where k is the smaller root of the equation Cx = ex - I if C > 1, and the larger root of x = Ce X - I if C < 1, where C is defined as in (i), Section 8