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I come across a question about calculating the expectation for random vectors
and I have no idea how to do with it.
Anyone could give me a hand? Thanks for your attention.
The PDF of , conditioned on , is Gaussian with mean vector and covariance matrix
and the PDF of and , given , are also both Gaussian:
We also have
are all known and is an identity matrix.
Now what is the conditional expectation of , given some
observed and , i.e.,
The answer is something like
But don't know how