"... and when we want to look at just a subset of the variables in a joint distribution, we have to sum over all the other variables: the probability that *X* is blue, is equal to the probability that both *X* is blue and *Y* is blue, *plus* the probability that *X* is blue and *Y* is red, *plus* ... and so on for all the values *Y* could take. We call this *marginalizing over* *Y* to get the *marginal distribution* for *X*. Note that you can think about this as taking an expected value. Does that make sense?"

"Ummm ... ye-es?"

"You don't sound very confident."

"The exact referent of the word *that* in 'Does that make sense?' was ambiguous, because it was preceded by a long, multi-part explanation. *Most* of the potential referents made perfect sense, but my response had to average over *all* of them, hence the hesitation and uncertain tone."