Quote by kasraa
Does it also imply:
[tex] E \left[ \left( x  E \left[ xZ \right] \right) ^2  Z \right] = E \left[ \left( x  E \left[ xZ \right] \right)^2 \right] [/tex]?
Is it correct?
Thanks.

As I said, I don't know what the double conditional on Z means. I can only guess that it might mean something like [tex]P_{kk}[/tex] which indicates the successor state to [tex]P_{kk1}[/tex]. If so, you need to introduce a system of subsripts.
Also, I don't see any problem to getting the MSE from any sample vector. It's the MMSE that can be a challenge.