Homework Help is Here – Start Your Trial Now!
Math
Statistics
We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%

We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

f(y): 1 T()√√ (1 + (y-μ)²)-¹.
Transcribed Image Text:f(y): 1 T()√√ (1 + (y-μ)²)-¹.
Question -200 Samples 1 deg. Freedom, unknown location Paremeter uit (1,1) a POF → f(y) = 1 T (²) √ (1 + (x-1)²) = 1 log ikinas f (Vi) (412) -√7) (1 + (Y-μ)²) = 1 (200 sommes) 1st- · 2 (M/Yi) = log f (Vi) = C-log (1 + (Vi _u)²) · 2 (MK²) (y) зм Ind. deristike 3 32" (MY) u 2.00 = log (f(x)) = log (it+ ₁ f(x)) = = = = log (f (vi)) = 200 ^ C → ²log (1 + (√²-1) ² 200 cancels since we mulive vbx -2 200 2 =X²-2²2 1 + (K-M) ² -each of the y different dotopar
Transcribed Image Text:Question -200 Samples 1 deg. Freedom, unknown location Paremeter uit (1,1) a POF → f(y) = 1 T (²) √ (1 + (x-1)²) = 1 log ikinas f (Vi) (412) -√7) (1 + (Y-μ)²) = 1 (200 sommes) 1st- · 2 (M/Yi) = log f (Vi) = C-log (1 + (Vi _u)²) · 2 (MK²) (y) зм Ind. deristike 3 32" (MY) u 2.00 = log (f(x)) = log (it+ ₁ f(x)) = = = = log (f (vi)) = 200 ^ C → ²log (1 + (√²-1) ² 200 cancels since we mulive vbx -2 200 2 =X²-2²2 1 + (K-M) ² -each of the y different dotopar
Expert Solution
Step 1

Given

Pdf 

Statistics homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS