is the relative entropy of the joint probability distribution P ( X , Y ) from the product P ( X ) P ( Y ) of the two marginal probability distributions — i.e. the expected number of extra bits that must be transmitted to identify X and Y if they are coded using only their marginal distributions instead of the joint distribution. Equivalently, if the joint probability P ( X , Y ) is known, it is the expected number of extra bits that must on average be sent to identify Y if the value of X is not already known to the receiver.