E[Y]=E[E[Y/X=x]] I always get confused regarding this. Random variable for inner "[E]" will be "Y" and outer "[E]" will be X. If anyone can help me regarding how to derive this step by step.
Just a quick comment - the property you're thinking of is E[Y] = E[E[Y|X]] - this is not equal to E[Y|X=x]. The derivation is fairly straightforward - WP has the derivation for the discrete case: http://en.wikipedia.org/wiki/Law_of_total_expectation#Proof_in_the_discrete_case It does the general case in the language of measure theory, but you might find it helpful to work through the continuous case using the discrete case as a guide.
