Homework Help is Here – Start Your Trial Now!
Math
Statistics
(a) Using FOIL, show that (Xi − X)² = Σ²₁(X² — 2X¿X + X²). (b) Show that (X? − 2X;X + X²) = {Σ²²_₁ X²} − nò. (c) Finally, show that S² || Σ (X - X)2 _ {Σ,X?} - nX2 n-1 n-1

(a) Using FOIL, show that (Xi − X)² = Σ²₁(X² — 2X¿X + X²). (b) Show that (X? − 2X;X + X²) = {Σ²²_₁ X²} − nò. (c) Finally, show that S² || Σ (X - X)2 _ {Σ,X?} - nX2 n-1 n-1

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%
STAT 3128 Homeowrk Section Question 1. Let X₁,..., Xn be a random sample from N(μ, o²). The sample mean X and sample variance S² are unbiased estimators for μ and o², respectively, where X = Ei=1 Xi Σ (X - X)2 = n n-1 (a) Using FOIL, show that Σ_₁(X; —– X)² = Σ²²_₁(X? — 2X;X + X²). (b) Show that ₁(X? − 2X¿Ã + X²) = {Σï_₁ X²} − nĂ². (c) Finally, show that S² 82 Σ? (X; — Ñ)² _ {Σ½_₁ X²} − nX² n - 1 n - 1
Transcribed Image Text:STAT 3128 Homeowrk Section Question 1. Let X₁,..., Xn be a random sample from N(μ, o²). The sample mean X and sample variance S² are unbiased estimators for μ and o², respectively, where X = Ei=1 Xi Σ (X - X)2 = n n-1 (a) Using FOIL, show that Σ_₁(X; —– X)² = Σ²²_₁(X? — 2X;X + X²). (b) Show that ₁(X? − 2X¿Ã + X²) = {Σï_₁ X²} − nĂ². (c) Finally, show that S² 82 Σ? (X; — Ñ)² _ {Σ½_₁ X²} − nX² n - 1 n - 1
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 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