Proof of identity $E[V | W] = E[E[V | U,W] | W]$

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What is the intuition and the proof behind the expression

$E[V | W] = E[E[V | U,W] | W]$

where $U,V,W$ are random variables. I know that $E[V | W]$ can be treated as a random variable which is a function of $W$ but I am having a hard time getting the intuition about the above expression of nested expectations.