Is there any mathematical association between the conditional expectation of a variable given another variable, and the unconditional expectation of that variable?
I realise that given a joint distribution between $A$ and $B$, we can find $E[A]$ by first finding the marginal distribution of $A$.
However, suppose we know what is $E[A|B]$, is it possible to obtain $E[A]$ from this alone using any mathematical property?