Hello I am struggling with the following question, can anybody help please?
Consider a positive real valued random variable $X$
Experiment A: Draw a sample of $X$ and create a square with it as the edge length, and call this square $S$.
Experiment B: Draw two independent samples of $X$ and create a rectangle with these two as sides, and call this rectangle $R$. Let $$A = E[\text{Area}(S)] (E - \text{Expectation})$$ and $$B = E[\text{Area}(R)]$$ What is relation between $A$ and $B$?
Edit: I have no idea how to approach this kind of questions any help is highly appreciated.
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$