Let the joint pmf of X and Y be (a) Are X and Y

QUESTION:

Let the joint pmf of \(X\) and \(Y\) be

\(f(x, y)=1 / 4, \quad(x, y) \in S=\{(0,0),(1,1),(1,-1),(2,0)\}\)

(a) Are \(X\) and \(Y\) independent?

(b) Calculate \(\operatorname{Cov}(X, Y)\) and \(\rho\).

This exercise also illustrates the fact that dependent random variables can have a correlation coefficient of zero.

Equation Transcription:

Text Transcription:

X  

Y  

f(x,y)=1/4, (x,y) in S={(0,0),(1,1),(1,-1),(2,0)}  

Cov⁡(X,Y)

rho