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 19:12Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 


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 $E[vX \ge x_0] = \frac{1}{P[X \ge x_0]} \int_{x_0}^\infty E[vX = x] P[x] \mathrm{d}x = \frac{ \int_{x_0}^\infty f(x)g(x) \mathrm{d}x}{\int_{x_0}^\infty f(x)\mathrm{d}x}$ 

