I am trying to understand Bayesian estimation and I come across this line in my lecture notes:

```
 θ(Bayesian) = E_θ|x[θ] =  E[π(θ|x)]

```

So it's meant to reader that the Bayesian estimator is the Conditional Expectation of the sample (x's) which equals the expectation of the posterior (3'rd expression). I understand the derivation up to this point but I dont see how the conditional expectation of theta:

So the middle expression "E\_θ|x[θ]" (should look like E underscore θ|x of θ) is:

Integral [θ · π(θ|x) dθ]

and somehow that equals the expectation of the Posterior i.e.

```
E[π(θ|x)]

```

Please help! I am hoping it is a simple answer cause there is no explanation between these steps.