# Conditional expectation from covariance matrix

Given a vector $$\mu = \{\mu_x \mu_y \mu_z\}$$ and an equivalent covariance matrix $$\Sigma$$, I used the following in Mathematica to compute the conditional expectation $$\mathbf{E}(Y|Y+Z)$$.

Expectation[
y \[Conditioned] y + z == y0 + z0 , {x, y, z} \[Distributed]
MultinormalDistribution[mu, sigma]]


Which produced the correct result.

As I try something a bit more tricky like $$\mathbf{E}(Y|(Y+Z)^2)$$ with the following:

Expectation[
y \[Conditioned] (y + z)^2 == (y0 + z0)^2 , {x, y, z} \[Distributed]
MultinormalDistribution[mu, sigma]]


Mathematica does not output a result.

I imagine Mathematica is capable of this computation so I must be inputting something in incorrectly. Is this possible to compute in Mathematica knowing Mean and Covariance Matrix?

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