# Covariance and conditional probability

This may be completely trivial, but wanted to understand the following better: Let's say we know the covariance of two random variables $X, Y$ - is there anything intelligent we can say about the expected value of $X$, given an observation $Y = y$?

I.e. what (if any) is the relationship of $cov(X,Y)$ and $\mathbb{E}(X|Y = y)$?

If required, we may assume that we know $\mathbb{E}X=\mu$ and $\mathbb{E}{Y}=\gamma$.

• Are you aware that E(X|Y) is a random variable, not a number? – Did Aug 10 '14 at 1:18
• You are right, thanks - edited the question to make it more precise. – wfh Aug 10 '14 at 1:24
