Question: Let X1, X2,..., Xn be an iid random sample where X: m Normalu, o2], p: unknown, and 02 unknown. {a} Find the MLE's for both

Let X1, X2,..., Xn be an iid random sample where X:

Let X1, X2,..., Xn be an iid random sample where X: m Normalu, o2], p: unknown, and 02 unknown. {a} Find the MLE's for both it and o2. Hint: The likelihood and loglikelihood functions for both will be the same. But when you get to Step 3, you'll get two expressions. One from taking the derivative with respectto pi. and the other by takingIr the derivative with respect to o2. fh] Show that the MLE 62 is a biased estimator for or2 when p is unknown. Calculate the value of the bias of 33, and calculate the mean squared error of $2. {c} Based on your answer to part [b], what would you need to do to the MLE d2 to create an unbiased estimator for us2 when u is unknown? Show that your new statistic based on the MLE 32 is unbiased. Hint: What is the name of that "new statistic\"? You've seen it before

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