0
$\begingroup$

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?

enter image description here

Edit:

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:

enter image description here

or am I missing something?

Improve this question
$\endgroup$
2
  • $\begingroup$ is this homework or self-study? If so, please tag your question accordingly $\endgroup$
    – jpmuc
    Commented May 18, 2014 at 17:13
  • $\begingroup$ exam revision looking at past papers. $\endgroup$
    – jshbrntt
    Commented May 18, 2014 at 17:22

1 Answer 1

Reset to default
0
$\begingroup$

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:

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

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.