An addendum to my previous post.
I realized the expression easily simplifies if homogeneity of
variance is assumed, where V(Z)|X=1 = V(Z)|X=0. Because this is an
assumption normally made in the context of my usage, I can proceed with
it. However, I am still curious about the original problem, and would
be interested in any thoughts on whether a closed form solution existed
for the parameters I needed (px, E(z), C(x,z), V(x), V(z))
Thanks,
-E
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