# Solved – Expectation with subscript

I have a question. A and B are normal distibutions.
how to calculate \$operatorname{E}_{A,B}[A^2]\$ does it scene that I drop the B in the statement or do I have to consider the B somehow ?

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The subscript just means that the expectation is with respect to the joint distribution of $$(A,B)$$. Use of the subscript does not add anything in this case, since there is nothing in the expectation that depends on the random variable $$B$$. In this case you have:
begin{equation} begin{aligned} mathbb{E}_{A,B}(A^2) &= int int a^2 p(a,b) da text{ } db \[6pt] &= int int a^2 p(a) p(b|a) da text{ } db \[6pt] &= int a^2 p(a) Big( int p(b|a) db Big) da \[6pt] &= int a^2 p(a) da \[6pt] &= mathbb{E}_A(A^2). \[6pt] end{aligned} end{equation}