Hey DerWundermann.
You need to find the joint distribution of X1 and Z and then from that calculate Cov(X,Y) = E[XY] - E[X]E[Y]
Remember that P(A|B) = P(A and B)/P(B) and that P(A) = Integral/Sum_out P(A|B=b)*P(B=b) for all appropriate b.
Hi Folks!
Let X1 have a chi-squared distribution with 1 degree-of-freedom.
Let Xn have a chi-squared distribution with n degrees-of-freedom.
Next, consider
Z = X1+Xn
Then, assuming that X1 and Xn are independent, Z has a chi-squared distribution with n+1 degrees-of-freedom.
Are you able to provide any comments on how to obtain
correlation(X1,Z)?
Cheers!
Der
Hey DerWundermann.
You need to find the joint distribution of X1 and Z and then from that calculate Cov(X,Y) = E[XY] - E[X]E[Y]
Remember that P(A|B) = P(A and B)/P(B) and that P(A) = Integral/Sum_out P(A|B=b)*P(B=b) for all appropriate b.
My comments in post #4 are wrong, but i haven't figured out why yet.
an alternative method which i think is valid and does not require calculating the joint distribution is: