Could someone help me with question 5.b. I understand that the probability of any of these occuring independently is 0.5 but how do I combine those into a joint distribution function?

Is $0.5 \cdot 0.5 \cdot 0.5 \cdot 0.5 = 0.0625$ correct?

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Is it more like this?

$S =$ Spam, $D =$ Dear, $F =$ Free, $H =$ Hot $$ P(S, D, F, H) = P(S) \cdot P(D | S) \cdot P (F | S, D) \cdot P(H | S, D, F) $$ Therefore:

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or am I missing something?

  • $\begingroup$ is this homework or self-study? If so, please tag your question accordingly $\endgroup$
    – jpmuc
    May 18, 2014 at 17:13
  • $\begingroup$ exam revision looking at past papers. $\endgroup$
    – jshbrntt
    May 18, 2014 at 17:22

1 Answer 1


Given the nature of the problem, I would rather structure the model as a Naive Bayes classifier, i.e. with edges going from Spam to Hot, Free and Dear. It's a modelling choice of course, but I think it makes more sense given the task at hand.

With this Naive Bayes structure, the joint probability distribution is then simply:

$$ P(Hot, Free, Dear, Spam) = P(Hot \ | \ Spam) \ P(Free \ | \ Spam) \ P(Dear \ | \ Spam) \ P(Spam) $$


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