Assignment 1Due Monday July. 7th Before ClassSuppose random variables X Y have t

Assignment 1Due Monday July. 7th Before ClassSuppose random variables X Y have the following probability distribution:Prob Y=0 Y=2 Y=3X=-2 0.2 0.2 0X=2 0.2 0 0.1X=4 0.2 0 0.1(10%)(1) Compute EX EY .(10%)(2) Compute VarX VarY .(10%)(3) Find probability distribution of XY .(10%)(4) Compute Cov(X; Y ).(10%)(5) Compute Corr(X; Y ). Are X and Y correlated? Why?(10%)(6) Are X and Y independent? Why?(10%)(7) Compute E(XjY = 3).(10%)(8) Find an estimator for EXY .(10%)(9) Find a t-statistic to test hypothesis H0 : EXY = 1 v.s. H1 : EXY 6= 1(10%)(10) Compute EYX and EYEX and nd estimators for them respectively.1