Question-31

The joint distribution of \(X\) and \(Y\) is given by \(f_{XY}(x,y) = \dfrac{x+y}{9}\), for \(x = 0,1,2\) ; \(y=0,1\). What is the value of Cov\((X,Y)?\)

• \(\dfrac{1}{27}\)

• \(\dfrac{-2}{27}\)

• \(\dfrac{2}{27}\)

• \(\dfrac{-1}{27}\)

Hint

Apply the formula : \(Cov(X,Y) = E[XY] - E[X] E[Y]\)

where, \(E[XY] = \sum xyf_{XY}(x,y)\)

\(E[X] = \sum x f_X(x)\) and \(E[Y] = \sum y f_Y(y)\)

Answer

• \(\dfrac{1}{27}\)

• \(\dfrac{-2}{27}\)

• \(\dfrac{2}{27}\)

• \(\dfrac{-1}{27}\)

Solution