Problem 9E

Let X1,..., Xn be a random sample from a N(0, σ2) population. Find the MLE of σ.

Answer:

Step 1 of 1:

Let X follows Normal distribution with Probability density function

f(x) =

The claim is to find the Maximum likelihood function (MLE) of .

The likelihood function is

L(x:) = ()

Take log on both sides

Log L(x:) = Log()

= -log (2- n log()

Differentiate with respect to and equate it to zero.

(-log (2- n log() ) = 0

Where, ( n log() ) = , (-log (2= 0 and () =

Therefore, - +

-n+ = 0

=

=

Maximum likelihood function (MLE) of is =