1.
[
P(A|BC) = frac{P(AB|C)}{P(B|C)}
]
2.
In EM algorithm, the usual expectation function can be written as follows:
[
egin{split}
Q( heta, heta^0) &= E_{h}left[P(mathbf{x},h| heta)|mathbf{x}, heta^0
ight] \
& = sum_{h}P(mathbf{x},h| heta)P(h|mathbf{x}, heta^0)
end{split}
]
where
$h$ : the hidden varible.
$ heta$ : the obvious varible.
$mathbf{x}$ : the observed data.
$ heta^0$ : the obvious varible calculated on the last.
3.
The inverse of a symmetrical matrix is still symmetrical.
That is because
[
(A^{-1})^T = (A^T)^{-1} = A^{-1}
]