Let X1,..., Xn be a random sample from a N(0, σ2) population. Find the MLE of σ.
Step 1 of 1:
Let X follows Normal distribution with Probability density function
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 =
Textbook: Statistics for Engineers and Scientists
Author: William Navidi
The answer to “Let X1,..., Xn be a random sample from a N(0, ?2) population. Find the MLE of ?.” is broken down into a number of easy to follow steps, and 17 words. This full solution covers the following key subjects: Find, let, mle, population, random. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 9E from 4.9 chapter was answered, more than 298 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 9E from chapter: 4.9 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.