) Let X1, ..., Xm be a random sample from a normal distribution with mean Hy and variance o. Also, let Yı,..., Y, be a random sample from a normal distribution with mean H2 and variance ož. Assume that the two samples are independent. Suppose we are interested in testing the hypothesis that the two means are equal, against a two-sided alternative. (a) Call the common mean w, ie. t = H2 = p. Write down the likelihood function and find the MLEs of pl, oſ and 0, assuming the null hypothesis is true. (b) Write down the likelihood ratio test statistic for this hypothesis test and the critical value for a test with a significance level of 0.05. i. Write down the likelihood in general case. ii. Find the MLE of M1, M2, o and oz. iii. Write down the likelihood ratio test statisti