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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

My answers are:

a. 3.611

b. 3.204

c. 3.611

d. 3.204

Thanks Again for your help.

I greatly appreciate it.

PS:

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

1 Answers 1

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For the normal distribution, the MLEs and the method-of-moments estimates are the same. You can prove that by doing some algebra. (It's quite a different situation from what happens with the uniform distribution, where the method-of-moments estimate of the upper endpoint can actually sometimes be less than some of the observed values, making it absurd to use such an estimate in practice.)

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    i thought that's what i did... hmmmmm... i'll study the symbols here first then i'll show the formula. thank you xabier and michael. you guys are great :)2012-04-07