Maximum Likelihood

[alakaboom1]

Find the maximum likelihood estimate for the parameter \(\displaystyle \mu\) of the normal distribution with known variance \(\displaystyle \sigma^{2} = \sigma_{0} ^{2}\)

This seems to be a conceptual question on maximum likelihood. But to be honest, I didn't really understand the concept too well in lecture. So, I'm hoping someone can walk me through this problem. Thanks!

 

[tkhunny]

Let's start with some theoretical background.

"Find the maximum likelihood estimate for the parameter of the normal distribution with known variance "

This is a very odd question. \(\displaystyle \mu\) is the obviosuly correct response.

Let's try this question, "Given a set of 'n' observations from a normal distribution with known variance and unknown mean, what is the maximum liklihood estimate of \(\displaystyle \mu\)?"

Give the difference of the two a little thought and let's see where that leads.

 

[royhaas]

In the normal distribution, the maximum likelihood estimator of the population mean is always the sample mean, unless the population variance is a function of the population mean.

 

[tkhunny]

For once, I know enough to challenge royhaas on a statistics question - not really a challenge, but it's as close as I have gotten. Here goes...

Well, that response hardly leads to a useful calculation exercise.

That's all I've got.