Given E[vX=x]=g[x] and the pdf of X (f[x]), how to calculate E[vx>=x0]? The pdf of V or the joint pdf of V,X are unknown. My guess is that this problem has no solution.
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closed as off topic by Scott Morrison♦ May 16 '10 at 19:12
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So if $p(v,x)$ is the unknown pdf, $f(x) = \int p(v,x) \mathrm{d}v$ $g(x) = E[vX=x] = \int v \ P[vX=x] \mathrm{d}v = \int v \ \frac{p(v,x)}{f(x)} \mathrm{d}v$ and then $E[vX \ge x_0] = \frac{1}{P[X \ge x_0]} \int_{x_0}^\infty E[vX = x] P[x] \mathrm{d}x = \frac{ \int_{x_0}^\infty f(x)g(x) \mathrm{d}x}{\int_{x_0}^\infty f(x)\mathrm{d}x}$ 

