Q: Supposing y ~ N4 (µ,∑) and
µ = (1 2 3 -2)'
∑ =\begin{pmatrix} 4 & 2 & -1 & 2\\ 2&6&3&-2\\ -1&3&5&-4 \\ 2 &-2 &-4 &4\\ \end{pmatrix}
What is
(i) f(y1 | y2, y3, y4)?
(ii) 12|34 ?
For (i), I am using the formula E(y|x) = µ_y + σ_yx '∑_xx^(-1)(x - µ_x)
where I let x = (y_2 y_3 y_4). What happens to my ∑_xx now? I would believe it is a partition of the current ∑ where taking the values from row 2 to row 4 and column 2 to column 4. But if I am taking that, then there is no sense in making it a conditional probability in the first place.
Please help. Thanks