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(
)...