Re: probability equation

On Oct 27, 9:47 pm, longf...@xxxxxxxxx wrote:
Hi,

I have already posted this in a german newsgroup but unfortunateley,
it seems to be somehow difficult or not correct. I found the following
statement in a paper and was wondering how the transformation was
done:
Let A, B, C and D be random variables. Further, let A = B + D. Then,
Pr[A=a|C=c] = \sum_b Pr[A=a|B=b] * Pr[B=b|C=c] = sum_b Pr[D=a-b] *
Pr[B=b|C=c]

Do you know why these equations should hold (or do they hold at all)?

The first equality doesn't look correct. Try a really simple case,
say:

A B C D Probability
- - - - -----------
0 0 0 0 p
1 0 1 1 1-p

Say a = 0, c = 0. Then Pr[A=a|C=c] = 1, while \sum_b Pr[A=a|B=b] *
Pr[B=b|C=c] = p.

Are you sure there weren't other conditions? I mean, the equations
weren't supposed to hold generally, but just for some particular
situation that the paper was describing?

.

Relevant Pages

  • Re: probability equation
    ... I have already posted this in a german newsgroup but unfortunateley, ... it seems to be somehow difficult or not correct. ... Let A, B, C and D be random variables. ...
    (sci.math)
  • probability equation
    ... I have already posted this in a german newsgroup but unfortunateley, ... it seems to be somehow difficult or not correct. ... Let A, B, C and D be random variables. ...
    (sci.math)