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We consider two random variables X and Y with simultaneous probability distribution p ( x , y ) = P ( X = x Y
We consider two random variables X and Y with simultaneous probability distributionp(x,y)=P(X=xY=y) given by this table:
x/y | 0 | 1 | 2 |
---|---|---|---|
0 | 0.05 | 0.25 | 0.1 |
1 | 0.1 | 0.05 | 0.1 |
2 | 0.25 | 0 | 0.1 |
a) Find the marginal probability distributions for X and Y. What isP(X=2Y=2)? Is X and Y independent random variables? Justify the answer.
b) Find the correlation between X and Y when you know the expectations are E(X)=0.95 and E(Y)=0.9, and the variace V(X)=0.747 and V(Y)=0.69.
c) Find conditional expectation E(Y|X = 2) and the conditional variance V(Y|X = 2)
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