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???