2. A continuous random variable X has a chi-square distributionwith degrees of freedom v if it has the pdf1X222T 5)-1x> 0f(x) =e 2,Show that E(X)%3D= v and var(X) = 2va.b. Using a sample of size n, obtain a method of momentestimate for vFrom (a) above, deduce thatr) = VTTC.

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2. A continuous random variable X has a chi-square distribution with degrees of freedom v if it has the pdf 1 X2 -1 f(x) = e 2, x> 0 2år () 22T Show that E(X) = v and var(X)= 2v a. %3D b. Using a sample of size n, obtain a method of moment estimate for v From (a) above, deduce that Г C.

2. A continuous random variable X has a chi-square distribution with degrees of freedom v if it has the pdf 1 X2 -1 f(x) = e 2, x> 0 2år () 22T Show that E(X) = v and var(X)= 2v a. %3D b. Using a sample of size n, obtain a method of moment estimate for v From (a) above, deduce that Г C.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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2. A continuous random variable X has a chi-square distribution
with degrees of freedom v if it has the pdf
1
X2
22T 5)
-1
x> 0
f(x) =
e 2,
Show that E(X)
%3D
= v and var(X) = 2v
a.
b. Using a sample of size n, obtain a method of moment
estimate for v
From (a) above, deduce that
r) = VTT
C.

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