Re: Help: Coding theory and Probability


Proginoskes wrote:
> blazer320@xxxxxxxx wrote:
> > I have a code C={000, 111}. Suppose v in C is sent and 110 is
> > received. What is the probability 111 was sent? Here p=.9
> > where p is the probability that a digit sent is the digit
> > received.
> >
> > Obviously an error occured in the channel with 110 as the only
> > 2 possible words that could have been sent are 000 and 111.
> > I don't really have much of a probability background, so I'm
> > at a loss as to how to compute this. I would really appreciate
> > someone showing me how to do this problem.
> >
> > I tried (.9*.9*.1)/(.9*.9*.1+.1*.1*.9) but that just equalled .9
so
> I
> > must have tried the wrong thing.
>
> I thought it was Bayes's Formula, which you almost have above.
> Bayes's Formula is:
>
> P(S111 : R110) = P(S111) * P (R110 : S111) /
> [P(S111) * P (R110 : S111) + P(S000) * P (R110 : S000)],
>
> where S111 is the event that 111 was sent, R110 is the event that 110
> was received, etc. and I've used : instead of the usual vertical bar
> "|".
>
> You've calculated P (R110 : S111) (.081) and P (R110: S000) (.009).
If
> we let q = P(S111), then the conditional formula reads:
>
> P(S111 : R110) = .081 q / (.081 q + .009 (1 - q)).
>
> I strongly suspect that there may be insufficient information here.

Yes, as you indicate with your unknown q, you need to know
what the probability was that 000 or 111 was sent. If the
sender never transmits 111, then the probability that the
received 110 indicates a sent 111 is obviously 0.

In the absence of other information to the contrary, it's
reasonable to assume the two codes are transmitted
equally often.

- Randy

.

Relevant Pages

  • Re: permutations problem, please help
    ... probability that two of the people would choose the same set? ... two four digit numbers. ... For example, if the duplicate occured at draw 3175, then ... I got this histogram for 1256 trials: ...
    (sci.math)
  • Re: permutations problem, please help
    ... Are you assuming that people choose numbers with a uniform probability ... The meaning of \ between the numbers is really just a divider. ... two four digit numbers. ... Does the fact that people are choosing but don't ...
    (sci.math)
  • Re: Randomness of digits within pi
    ... Thus if we pay 100 business lunches in $ or convert the amount ... And *if* there is a such unit independant probability distribution ... then the probability of beginning with digit d must be proportional ...
    (sci.math)
  • Re: Std.dev. for skewed data
    ... digits"R.E.Greenwood determined that the waiting time for a ... given digit to appear in random draws with replacement has a mean of ... Is it meaningful to calculate probability of greater than 1.616 ... (not a given digit, which is 10) ...
    (sci.stat.math)
  • Re: permutations problem, please help
    ... or answer it for me or chow me how to do it? ... probability that two of the people would choose the same set? ... two four digit numbers. ... Does the fact that people are choosing but don't ...
    (sci.math)