Suppose Z1 and Z2 are two standard norm random variables. In addition suppose cov(Z1,Z2)=p. Show (Z1-pZ2)/sqrt(1-p^2)and...

Suppose Z1 and Z2 are two standard norm random variables. In addition suppose cov(Z1,Z2)=p.

Show (Z1-pZ2)/sqrt(1-p^2)and Z2 are standard normally distributed
Show (Z1-pZ2) )/sqrt(1-p^2)and Z2 are independent. Hint : Two random normal variables are independent as long as they are uncorrelated
Show (Z1^2+Z2^2-2pZ1Z2)/(1-p^2) is Chai square distribution

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orchestra answered 1 year ago

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