Making Sense

"... 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."

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