T
Torgny
I have proved (8.1). However I am trying to prove that
##\bar{X},X_i\bar{X},i=1,...,n## has a joint distribution that is multivariate normal. I am trying to prove it by looking at the moment generating function:
##E(e^{t(X_i\bar{X})}=E(e^{tX_i})E(e^{\frac{t}{n}\sum_{i=1}^n X_i})##
I am trying to use the moment generating function because there is only one moment generating function for a given probability distribution and this also holds for multivariate distributions. But I fail at obtaining a moment generating function. The mgf to ##E(e^{tX_i})## is simply the mgf to the normal distribution but I cant get a moment generating function to ##E(e^{\frac{t}{n}\sum_{i=1}^n X_i})## which from the answer in the text i guess should be a multivariate normal distribution.
Can someone help out?
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