Consider the two statements. $$\begin{aligned} S_1 :& \quad \text{There exist random variables } X \text{ and } Y \text{ such that} \\ & \quad \left(\mathbb{E}\left[(X - \mathbb{E}(X)) (Y - \mathbb{E}(Y))\right]\right)^2 > \mathrm{Var}[X] \, \mathrm{Var}[Y] \\ S_2 :& \quad \text{For all random variables } X \text{ and } Y, \\ & \quad \mathrm{Cov}[X,Y] = \mathbb{E}\left[|X - \mathbb{E}[X]| \, |Y - \mathbb{E}[Y]|\right] \end{aligned}$$ Which one of the following choices is correct?

Consider the two statements. aligned S1 :& There exist random variables X and Y such that \\ & ( E [(X - E(X)) (Y - E(Y)) ] )2 > Var[X] \, Var[Y] \\ S2 :& For all random variables X and Y, \\ & Cov[X,Y] = E [|X - E[X]| \, |Y - E[Y]| ] aligned Which one of the following choices is correct?

Topic-wise GATE CS PYQs with verified steps