2 upvotes, 1 direct replies (showing 1)
View submission: What is the relationship between Conditional Probability and "Correlation"?
Note it's possible for random variables to be dependent and uncorrelated: let X ~ N(0,1), then X and X^2 are uncorrelated but directly dependent, since Cov(X,X^(2)) = E[X(X^2 - 1)] = E[X^(3)] = 0.
For this reason the connection between correlation and conditioning is deeply messy. You can work it out -- only particular pairs of random variables can be uncorrelated but dependent, and this implies something about the relationship between correlation and conditioning by decomposing the space of all possible "conditionings" -- but more than likely what you want is the relationship between independence and conditioning.
Which is immediate: doesn't matter if you condition on something independent or not. X, Y independent implies X | T(Y) = X for any observation T of Y.
Comment by alik604 at 07/10/2021 at 18:16 UTC
1 upvotes, 0 direct replies
Thank you very much