Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A have found an alternative definition of independency for a given conditional probability $P(A|B)$, they are independent, iff all columns of the probability table are equal.

What does equal mean in this case? For instance

$$P(A|B) = \begin{pmatrix}0.3 & 0.7\\0.7 & 0.3\end{pmatrix}$$

Where $A$ is associated with the columns and $B$ is associated with the rows, for instance $P(A=0|B=1) = 0.7$ read at the bottom on the left.

share|improve this question
add comment

2 Answers 2

up vote 1 down vote accepted

It means that $P(A=i\mid B=j)=P(A=i\mid B=k)$ for every $i$, $j$ and $k$.

share|improve this answer
    
+1 Easy to comprehend notation –  Mahoni Jun 9 '12 at 15:06
add comment

Independence means P(A and B)=P(A|B)P(B)=P(B|A)P(A)=P(A)P(B). I think this is just a way of showing it in a table when A and B consists of {0, 1} with certain probabilities associated with the 4 joint occurrences {0, 0}, {0, 1}, {1. 0}, {1, 1}.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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