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Math Help - How to describe the probabilty in this case?

  1. #1
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    How to describe the probabilty in this case?

    If we receive a flow of bits of a particular length, how to describe it in function of the length L?
    I am interested in the description of the probability of receiving the sequence "10".
    p1: Probability of receiving 1
    p0: Probability of receiving 0
    px: Probability of receiving whatever

    If L=3, we can have:
    10x
    x10
    so, the probability is p=2*p1*p0*px

    If L=4,
    10xx
    x10x
    xx10
    1010
    Here, the probability is p=3*p1*p0*(px^2)+(p1*p0)^2

    If L=5,
    10xxx
    x10xx
    xx10x
    xxx10
    1010x
    10x10
    x1010
    In this case, p=4*p1*p0*(px^3)+3*((p1*p0)^2)*px

    ...

    How to describe the probability in general, using L as variable???
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  2. #2
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    Re: How to describe the probabilty in this case?

    Quote Originally Posted by jgonzalf View Post
    If L=4,
    10xx
    x10x
    xx10
    1010
    Here, the probability is p=3*p1*p0*(px^2)+(p1*p0)^2
    I don't think this is right because both 10xx and xx10 include 1010.

    It is easy to calculate strings that don't contain 10. Such strings have the form 0...01...1 where each of the two parts can be empty.
    Thanks from jgonzalf
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  3. #3
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    Re: How to describe the probabilty in this case?

    You are right, emakarov, I will try to reformulate the problem. Thanks a lot.
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  4. #4
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    Re: How to describe the probabilty in this case?

    Quote Originally Posted by jgonzalf View Post
    You are right, emakarov, I will try to reformulate the problem.
    Please explain exactly what you are looking for is a bit-string.
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