Given E[v|X=x]=g[x] and the pdf of X (f[x]), how to calculate E[v|x>=x0]? The pdf of V or the joint pdf of V,X are unknown. My guess is that this problem has no solution.



Conditional expectation
So if $p(v,x)$ is the unknown pdf, 


$f(x) = \int p(v,x) \mathrm{d}v$


$g(x) = E[v|X=x] = \int v \ P[v|X=x] \mathrm{d}v = \int v \ \frac{p(v,x)}{f(x)} \mathrm{d}v$


and then


$E[v|X \ge x\_0] = \frac{1}{P[X \ge x\_0]} \int\_{x\_0}^\infty E[v|X = x] P[x] \mathrm{d}x = \frac{ \int\_{x\_0}^\infty f(x)g(x) \mathrm{d}x}{\int\_{x\_0}^\infty f(x)\mathrm{d}x}$


