Maximum Likelihood

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!

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.

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.

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.