A Math Problem

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z=v+e2

y=v+e1+e2

v, e1, e2 are normally distributed with means (u,0,0) and variances (sigma_v, sigma_e1, sigma_e2)

f=E(v|y, and z belong to NG) where NG is an unknown set that I wish to solve for.

a*E[(v-f)^2|z]<b determines the NG set.

How do I solve for the NG set? Thank you!

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