Please use Python or 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:Screenshot $1402-11-24$ at $17\mathrm{.}53\mathrm{.}32-1.$png

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

Using the data in the table, calculate the values of E$($XY$),$ COV$($X$,$Y$),$ and CORR$($X$,$Y$)$

Are X and Y independent of each other? Explain why using the result from previous parts.