Statistics - II problem

[natyfaty]

Q2)
Suppose you have a random variable A which is the sum of 9 squared IID N(0,1) random variables and another random variable B which is the sum of 25 squared IID N(0,1) random variables. Further, denote Z to be an N(0,1) random variable. Define two additional random variables as follows:

• X=Z/sqrt{A/9}
• Z=(A/9)/(B/25)

where sqrt{} is the square root function. Denote the Normal, Chi-square, t, and F distributions to be N(mu,sigma), ChiSq(df), t(df), and F(df1,df2), respectively. Let "~" further denote "is distributed." What are the distributions of A, X, and Z?

A~F(9,25), X~t(9), Z~F(3,5)
A~ChiSq(3), X~t(5), Z~F(9,25)
A~ChiSq(9), X~N(0,1), Z~F(3,5)
A~ChiSq(9), X~t(9), Z~F(9,25)

 

[Deleted member 4993]

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