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???

Re: How to describe the probabilty in this case?

Quote:

Originally Posted by

**jgonzalf** 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.

Re: How to describe the probabilty in this case?

You are right, emakarov, I will try to reformulate the problem. Thanks a lot.

Re: How to describe the probabilty in this case?

Quote:

Originally Posted by

**jgonzalf** You are right, emakarov, I will try to reformulate the problem.

Please explain exactly what you are looking for is a bit-string.