# Mean and Variance of Methods of Moment Estimate and Maximum Likelihood Estimate of Normal Distribution.

I just wanna verify if I answered this question correctly.

The following numbers are taken from a population having normal distribution with mean and variance :

5.3299 4.2537 3.1502 3.7032 1.6070 6.392 3.1181

6.5941 3.5281 4.7433 0.1077 1.5977 5.4920 1.7220

4.1547 2.2799

a. Find the maximum likelihood estimate of the mean

b. Find the maximum likelihood estimate of the variance

c. Find the method of moments estimate of the mean

d. Find the method of moments estimate of the variance

a. 3.611

b. 3.204

c. 3.611

d. 3.204

I greatly appreciate it.

PS:

I am unsure cause MLE and MME for the mean and variance of the Normal Distribution is the same.

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Your answers are numerically correct. Your computation of the MLEs seems fine. But I don't understand your derivation of the MMEs very well. You should identify the population moments with the sample moments. If you have two parameters to estimate (as it is the case) you need two equations, hence you put (sample mean)=(E(X)) and (sample variance)=(var(X)) [or maybe $(1/n)\sum X_i^2=E(X^2)$, depending on your textbook.] – Xabier Domínguez Apr 7 '12 at 17:42