Probability distribution Assignment 1

Assignment 1

Suppose random variables X, Y have the following probability distribution:
Prob Y=0 Y=2 Y=3
X=-2 0.2 0.2 0
X=2 0.2 0 0.1
X=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(X|Y = 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 E
Y
X
and EY
EX
and find estimators for them respectively.