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jimholt
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Not really a homework question, but here goes...
If we have two (binary) random variables X and Y, and we know the probability mass function for X, as well as the correlation between X and Y, can we find the probability mass function for Y?
Let f(x) be the mass function for X and g(y) be the mass function for Y. Let g(1) = q and g(0) = 1-q. Given f(1) = p and f(0) = 1-p, and that the correlation between X and Y is c, can we find q as a function of p and c (only)?
Let h(x,y) be the joint distribution of X and Y. We can show that that Cov(X,Y) = h(1,1)-pq, and so Corr(X,Y) = [h(1,1)-pq]/sqrt[pq(1-p)(1-q)] = c.
Where to go from there? Seems as if we have one equation with two unknowns. (Is there another equation lurking somewhere?)
Thanks for any help folks.
Homework Statement
If we have two (binary) random variables X and Y, and we know the probability mass function for X, as well as the correlation between X and Y, can we find the probability mass function for Y?
Homework Equations
Let f(x) be the mass function for X and g(y) be the mass function for Y. Let g(1) = q and g(0) = 1-q. Given f(1) = p and f(0) = 1-p, and that the correlation between X and Y is c, can we find q as a function of p and c (only)?
The Attempt at a Solution
Let h(x,y) be the joint distribution of X and Y. We can show that that Cov(X,Y) = h(1,1)-pq, and so Corr(X,Y) = [h(1,1)-pq]/sqrt[pq(1-p)(1-q)] = c.
Where to go from there? Seems as if we have one equation with two unknowns. (Is there another equation lurking somewhere?)
Thanks for any help folks.
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