Homework Help is Here – Start Your Trial Now!
Math
Statistics
(i) Find E(X) and var(X). (ii) Using Σ(X; – X)2 = Σ{(X; – μ) + (μ – Χ)}2 show that n n Σ(x; − x)2 = Σ(X; - μ) – n(Χ - μ). i=1 i=1 By taking expectations show that E(S2) = 62.

(i) Find E(X) and var(X). (ii) Using Σ(X; – X)2 = Σ{(X; – μ) + (μ – Χ)}2 show that n n Σ(x; − x)2 = Σ(X; - μ) – n(Χ - μ). i=1 i=1 By taking expectations show that E(S2) = 62.

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%
Question 2 Suppose X₁,..., Xn is a random sample from a distribution with mean µ and variance o². Let X = Σï=1 X₁/n and S² = Σï_1(Xį – X)²/(n − 1) be the sample mean and variance. (i) Find E(X) and var(X). (ii) Using Σ(Xį – X)² = Σ{(Xi − µ) + (μ − X)}² show that n n Σ(X; - X)² = [(X; − µ)² – n(X − µ)². − – – - i=1 i=1 By taking expectations show that E(S²) = o².
Transcribed Image Text:Question 2 Suppose X₁,..., Xn is a random sample from a distribution with mean µ and variance o². Let X = Σï=1 X₁/n and S² = Σï_1(Xį – X)²/(n − 1) be the sample mean and variance. (i) Find E(X) and var(X). (ii) Using Σ(Xį – X)² = Σ{(Xi − µ) + (μ − X)}² show that n n Σ(X; - X)² = [(X; − µ)² – n(X − µ)². − – – - i=1 i=1 By taking expectations show that E(S²) = o².
Expert 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