So P where P is Probability so P(X) = Prob(X) = P(X|I) = The Probability of Event X occurring:

latex formula 1

how can you derive this from P(X) = P(X,Y) $\cap$ P(X,$\bar{Y}$)?

Thank you,

Note: sorry it should be P(X) in the first one, it's the same X. X and Y are events, so it is events $Y_1, Y_2,Y_3 ... Y_m = \{Y_k\}$

This ideally is the beginning of the marginalization equation to get $ \int_{-\infty}^{+\infty} prob(Y|X)\ dY = 1$.

  • $\begingroup$ I take it $P(X,Y)$ is a number, but I don't know what you mean by the intersection of two numbers. $\endgroup$ – Gerry Myerson May 16 '12 at 4:12
  • 2
    $\begingroup$ Que? Probabilities are numbers. $Y$ may be an event, but $P(Y)$ is a number, and so, I expect, is $P(X,Y)$, although you haven't told us what $P(X,Y)$ means, so it's hard to be sure. Take some time to think your question through, and try again when you understand what you are actually trying to ask. $\endgroup$ – Gerry Myerson May 16 '12 at 4:21
  • 1
    $\begingroup$ @Eiyrioü von Kauyf : I think you must have meant $P((X\cap Y)\cup(X\cap \bar{Y}))$. Notice that in that expression the letter $P$ appears only ONCE. Notice also which ones say $\cap$ and which ones say $\cup$. One may write $P(A\cup B)=P(A)+P(B)$, but one should never write $P(A)\cup P(B)$ or the like---that is nonsense. $\endgroup$ – Michael Hardy May 16 '12 at 4:28
  • $\begingroup$ Satisfied with my answer? $\endgroup$ – Did Sep 19 '12 at 18:17

Let me recommend to get acquainted with Bayes' rule.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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