We all know that the covariance between two variables is defined as:
$Cov(X_{i},Y_{i}) = E[(X_{i}-\mu_{x})(Y_{i}-\mu_{Y})]$
Now I have seen this "simplification":
$E[(X_{i}-\mu_{x})(Y_{i}-\mu_{Y}) = E[(X_{i}-\mu_{x})Y_{i})]$
I get that you can simplify that to the usual covariance formula $E[(X_{i}-\mu_{x})Y_{i})]=E(X_{i}Y_{i})-E(X_{i})E(Y_{i})$
I wanted to ask you whether this always holds; or asked differently: When does the specification from above not apply? (This might be obvious but I am kind of confused right now, sorry). Thanks in advance!