# given an EPR pair, how do I calculate expectation values?

given A and B share EPR pairs $$(|00⟩+|11⟩)/√2$$

Here A is the 1st-qubit while B is the 2nd-qubit. And, both A and B are free to measure their own qubit with the following measurement settings

A measures with $$[|0⟩,|1⟩]$$ or $$[|+⟩,|−⟩]$$

B measures with $$[sin(3π/8)|0⟩+cos(3π/8)|1⟩,−sin(π/8)|0⟩+cos(π/8)|1⟩]$$ or $$[sin(π/8)|0⟩+cos(π/8)|1⟩,−sin(3π/8)|0⟩+cos(3π/8)|1⟩]$$

$\left[sin\left(\pi /8\right)|0⟩+cos\left(\pi /8\right)|1⟩,-sin\left(3\pi /8\right)|0⟩+cos\left(3\pi /8\right)|1⟩\right]$

So, let $$Ψ=(|00⟩+|11⟩)/√2$$

How do I calculate the expectation value, if A measures in 

$\left[|0⟩,|1⟩\right]$

basis and b measures in $$[sin(3π/8)|0⟩+cos(3π/8)|1⟩,−sin(π/8)|0⟩+cos(π/8)|1⟩]$$ basis?

I know that expectation value is  in this format $$E=<Ψ|x|Ψ>$$ , I would like to know what should be in place of $$x$$ and how to find it ?