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Calculation of an "unconstrained" normal distribution (starting from a censored one)
Assume that two r.v. $W$ and $Y|W=w$ with
(1) $W \sim \text{N}(\mu_w,\sigma_w^2)$ (iid)
(2) $Y|W=w \sim \text{N}(w,\sigma_y^2)$ (iid)
Further we only observe $Y$ if $Y$ is less then $W$, i.e.,
(3)...
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