Homework SourseCovariance question PX113 PX013 YX2 is X and Y independentSo
Covariance question :P(X=+-1)=1/3, P(X=0)=1/3, Y=X^2, is X and Y independent?
Solution
Thus we find E(XY) =0
And E(x) =0 and E(Y) =1/3
Cov = E(xy)-E(x)E(y)=0-0 =0
So X and Y are independent.
| x | -1 | 0 | 1 | y | 0 | 1 | ||
| p | 1/3 | 1/3 | 1/3 | 1 | p | 1/2 | 1/3 | 1 |
| xp | - 1/3 | 0 | 1/3 | 0 | y0 | 0 | 1/3 | 1/3 |
| x | -1 | 0 | 1 | |||||
| y | ||||||||
| 0 | 0 | 1/3 | 0 | 1/3 | ||||
| 1 | 1/3 | 0 | 1/3 | 2/3 | ||||
| 1/3 | 1/3 | 1/3 | 1 | |||||
| xy*p | 0 | 0 | 0 | |||||
| - 1/3 | 0 | 1/3 | 0 | |||||
