Let x1,dots,xn be a random sample from a N(mu ,sigma 2) population. Find the MLEs of mu and of sigma . (Hint: The likelihood function is a function of two parameters, mu and sigma . Compute partial derivatives with respect to mu and sigma and set them equal to 0 to find the values hat(mu ) and hat(sigma ) that maximize the likelihood function.)
2. Let X1,, Xn be a random sample from a N(, o2) population. Find the MLEs of and of o. (Hint: The likelihood function is a function of two parameters, and o. Compute partial derivatives with respect to and and set them equal to 0 to find the values and that maximize the likelihood function.)