10 Suppose that X and Y are discrete random variables having

10. Suppose that X and Y are discrete random variables having following joint pmf, where the rows are X and the columns are Y (a) Compute the marginal probability mass functions of X and Y, fx(x) and fy(y). (b) Find the covariance of X and Y. (e) Are X and Y independent? why?

Solution

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E(xy) = 1/3

E(x) E(y) = 0

As both are not equal X and Y are not independent.

x	-1	0	1	Total
y
0	0	1/3	0	1/3
1	1/3	0	1/3	2/3
Total	1/3	1/3	1/3	1
marginal density of x
x	-1	0	1	Total
Prob	1/3	1/3	1/3	1
X*p	- 1/3	0	1/3	0
x^2*p	1/3	0	1/3	2/3
Mean x	0
Var x	2/3