Question: If X = X 1 , ,X p are jointly normal with zero mean, show that the joint cumulant generating function, logE, exp(ijY ij )

If X = X 1

, …,X p

are jointly normal with zero mean, show that the joint cumulant generating function, logE, exp(ξijY ij

) of Y i,j = X iX j

is KY (ξ) = −1 1

2 log |I − 2ξκ|. Hence derive the cumulant generating function for the Wishart distribution.

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