# If $X_1, \ldots, X_N$ are NOT identically distributed nor independent, how would the $E(X)$ be different than what we have normally?

Suppose $$X_1, \ldots, X_N$$ are NOT identically distributed nor independent. Now, suppose I wanted to compute expectations, such as:

$$E(X|Z)$$

where Z is another variable. Does this change anything than what we are used to?

• What exactly is $X$ ? And also how do you solve this problem when they are iid ? – P. Quinton Feb 11 at 13:44
• $X$ are any arbitrary covariate specification. Under iid I would assume that the iterated expectations would follow, and hence I could do iterated expectations on the above. But, with the very action of iterated expectations, does it implicitly require iid? – user321627 Feb 11 at 13:50
• This is unclear to me, can you provide a short example ? – P. Quinton Feb 11 at 13:54
• I have the impression that $X$ is a random variable while $X_n$ is a sample of $N$ draws. – Bertrand Feb 11 at 13:58
• I don't think this is answerable until you say what the relation between the $X_i$ and $X$ is. Usually when people use this kind of notation the $X_i$ represent a random sample from a variable $X$. You say that your $X_i$ can have a different distribution to $X$, but then what are you assuming about the distributions they have? Clearly without some assumption these $X_i$ can tell you nothing. – Matthew Towers Feb 11 at 14:40