In [1, p. 61 exercise 3.8] we are asked to prove that the sample mean is a sufficient statistic for the mean under the conditions of [1, p. 61 exercise 3.4]. Assuming that $\sigma^{2}_{x}$ is known. We are asked to find the MLE of the mean by maximizing $p(\hat{\mu}_{x},\mu_{x})$. read the conclusion >