LDP correlation problem

If we have the next case:

• \(X^1\) has a uniform distribution on \([0,1]\)
• Explanatory variables are perfectly correlated \(X^1=X^2\)

And we calculate the LDP for \(X^1\) function:

\[ g_{LD}^{1}(z) = E_{X^2|X^1=z}(z+X^2) = z + E_{X^2|X^1=z}(X^2) = 2z. \]

The value reported is twice larger than the correct one.