# Help! A question of MLE

#### GretaGarbo

##### Human
There is no theta in that density. Be careful with what you write!

(But is it not pretty obvious? What happens if you take the log?)

#### Lawrence222

##### New Member
There is no theta in that density. Be careful with what you write!

(But is it not pretty obvious? What happens if you take the log?)
I wrongly wrote lamda in the place of theta, a little error. But the question is that I don't know how to tackle with the absolute value of (x-θ) after taking the log and summing up

#### Dason

##### Ambassador to the humans
Can you show us what you have so far.

And completely unrelated... What properties do you know about the sample median?

#### Lawrence222

##### New Member

This is as far as I can do with it

#### Lawrence222

##### New Member
Can you show us what you have so far.

And completely unrelated... What properties do you know about the sample median?
Yes, the MLE is the median of the sample, but why?

#### Dason

##### Ambassador to the humans
Have you been tasked with or at least told that the median minimizes the mean absolute deviation?

#### Archidamus

##### Member
Think Calc I, how do you find a maximum? Find the maximum of Ln[L(theta)], that gives you the theta value that is the 'best estimator'.

#### Dason

##### Ambassador to the humans
Think Calc I, how do you find a maximum? Find the maximum of Ln[L(theta)], that gives you the theta value that is the 'best estimator'.
Have you tried this particular problem?

#### Lawrence222

##### New Member
Have you been tasked with or at least told that the median minimizes the mean absolute deviation?
The first time I heard such a conclusion，but it is a good hint that we only need to prove that the minimum of the the mean absolute deviation is the median. Case closed then