Question

If X and Y are two random variables with the joint probability density function
f(x,y)=\left\\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.
then $E[X|Y=\frac{1}{2}]$ will be

• A. $\frac{5}{9}$
• B. $\frac{4}{9}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

Answer: (A)

$\frac{5}{9}$

Answer 2

The correct option is (A) : $\frac{5}{9}$.