Help with chi square distribution

  • Thread starter sneaky666
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  • #1
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How do i show that the a [X1 has a chi square distribution with n degrees of freedom] + [X2 has a chi square distribution with m degrees of freedom] is a [X1+X2 has a chi square distribution with n+m degrees of freedom]?

How can i use moment generating functions to do this?
 

Answers and Replies

  • #2
statdad
Homework Helper
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Yes.
 
  • #3
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How do i show that the a [X1 has a chi square distribution with n degrees of freedom] + [X2 has a chi square distribution with m degrees of freedom] is a [X1+X2 has a chi square distribution with n+m degrees of freedom]?

How can i use moment generating functions to do this?

MX1=(1-2t)-n/2
MX2=(1-2t)-m/2

MX1+X2=MX1*MX1= (1-2t)-(n+m)/2

which is the MGF of a chi-square distribution with (n+m) degrees of freedom.

That's all I can come up with...not terribly good with this....
 
  • #4
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How do i show that the a [X1 has a chi square distribution with n degrees of freedom] + [X2 has a chi square distribution with m degrees of freedom] is a [X1+X2 has a chi square distribution with n+m degrees of freedom]?

How can i use moment generating functions to do this?

If you want to show that a given set of random variables has a chi square distribution and that these distributions are additive you need to start with the Gaussian and then derive the characteristic function from the MGF.

http://www.planetmathematics.com/CentralChiDistr.pdf
 

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