Let $X_1$ be a continuous random variable with pdf $f(x)=\frac{2}{x^3},~~~~x>1$. $0 $ otherwise. Additionally the random variable $X_2$ is defined as $X_2=I_{[1,2]}(x)$. ($I$ := Indicator function)
Find $E(X_1X_2)$
I tried this $E(X_1X_2)=E(E(X_1X_2|X_1))=E(X_1E(X_2|X_1))$
My question is how do I find the function $f_{X_2|X_1}(X_2|X_1)$ when $X_1$ is continuous amd $X_2$ discrete? or I have to use law of iterated expectations?
Thanks