I'm not sure if this can be solved, I've used law of iterated Expectations to get $\textrm{E}[Q]$ but I am unsure how to proceed from here.
Many thanks for any help.
2026-04-13 02:24:31.1776047071
If $\textrm{E}[Q|P] = 3P+7$, $\textrm{E}[P]=2$ and $\textrm{E}[P^2]=8$ what is $\textrm{E}[PQ]$, can this be solved?
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First, multiply the first equation by $P$: $$PE[Q|P] = 3P^2 + 7P$$ But we know that $PE[Q|P] = E[PQ|P]$, so now we have $$E[PQ|P] = 3P^2 + 7P$$ and we get the answer by taking the expectation in the last equation.