j******a
发帖数: 1599 | 1 Using the joint characteristic function show that if X1, X2, X3, X4 are
jointly Gaussian (correlated) random variables with zero mean, then
E[X1X2X3X4] = E[X1X2]E[X3X4] + E[X1X3]E[X2X4] + E[X1X4]E[X2X3]
TIA | r******u
发帖数: 50 | 2 You can find a proof for a more general result in this paper:
W. Bar and F. Dittrich. "Useful formula for moment computation of normal ran
dom variables with non-zero means," IEEE Trans. Automat. Contr. vol. AC-16,
pp. 263-265, 1971.
【在 j******a 的大作中提到】
: Using the joint characteristic function show that if X1, X2, X3, X4 are
: jointly Gaussian (correlated) random variables with zero mean, then
: E[X1X2X3X4] = E[X1X2]E[X3X4] + E[X1X3]E[X2X4] + E[X1X4]E[X2X3]
: TIA
| H****h
发帖数: 1037 | 3 Find iid N(0,1) r.v.: Z1, Z2, Z3, Z4, such that every X is a linear span of
Z's.
【在 j******a 的大作中提到】
: Using the joint characteristic function show that if X1, X2, X3, X4 are
: jointly Gaussian (correlated) random variables with zero mean, then
: E[X1X2X3X4] = E[X1X2]E[X3X4] + E[X1X3]E[X2X4] + E[X1X4]E[X2X3]
: TIA
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