Hello Everyone!

I just want to make sure the following are correct:

$\displaystyle p_{A|B|C}=p_{A|B,C}$? And when does $\displaystyle p_{A|B,C}=p_{A|B}$?

$\displaystyle p_{A}\, p_{B|A}+p_{\bar{A}}\, p_{B|\bar{A}}=p_{B}$?

If two RVs are uncorrelated then their covariance is zero?

If two RVs are uncorrelated doesn't mean that they are independent? (but why?)

Thanks!