Question

A joint density function of random variable $X$ and $Y$ is given by $f(x,y)=\begin{cases}kx & \text{for } 0<x<1, 0<y<1 \\ 0 & \text{otherwise}\end{cases}$ then $Cov(X,Y)$ is

• A. $-1/6$
• B. $1/6$
• C. $0$
• D. $2/3$

Hint:

Always check for factorization first! If $f(x,y) = f_X(x) f_Y(y)$, then $X$ and $Y$ are independent, and you can immediately conclude that $Cov(X,Y) = 0$ and the correlation coefficient $\rho = 0$ without performing any integration.

Answer 1

The Correct Option is C