Consider the two statements.

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]|]

Which one of the following choices is correct?

An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following option is/are correct?

A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that, its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.