Please use

Matlab for all calculations and output. Submit your scripts $/.$m files as $.$PDF with yoir

submission.

Given that $x$ and $Y$ are two discrete random variables, and the table below is the joint probability distribution

for these variables:

I. Using the data in the table, calculate the values for $E(x),E(Y),$Var$(x),$ and Var$(Y).$

II$.$ Using the data in the table, calculate the values of $E(xY),$COV$(x,Y),$ and CORR$(x,Y)$

III. Are $x$ and $Y$ independent of each other? Explain why using the result from previous part