This should be relatively easy question but my math skills are rather limited.
Assume a that i is uniformly distributed between $\ [0,3] $
Also, assume that there is a price such that:
$$p \ge E[v * i | w * i \le p]$$
v and w are two unknown parameter with $\ w \gt v $. How do I calculate the conditional expectation of this formula, and how I handle the fact that the price parameter conditions i?
Assuming that $w,v$ are deterministic and for simplicity both $w,v>0$.
If $I \sim U(0,3)$, then $vI \sim U(0,3v)$ and $P(vI|wI \leq p) \sim U(0,\frac{vp}{w})$. Therefore $$\mathrm E[vI|wI \leq p] = \frac{vp}{2w}.$$ From this you can see the contidition under which such $p$ exists.