Suppose random variables

Assignment 1

Due Monday July. 7th Before Class

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(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 EY

X and EY

EX and nd estimators for them respectively.

1