Given $n$ independent random variables, $X_1, X_2, ..., X_n$ , each having a normal distribution, why is it that the following expectation holds?
$$E[(X_i - \mu)(X_j - \mu)] = 0$$
where $i \neq j$
I saw this statement in a proof explaining why we divide by $n-1$ when computing the sample variance and of course there was no explanation. An intuitive explanation and/or a link to more detailed information about why this is true would be greatly appreciated