Question 3.7 on set5

Question 3.7 on set5

par Gerry Windiarto Mohamad Dunda,
Number of replies: 1

When patterns have some overlap, should the mean become non-zero? My understanding is that when there is overlap, the patterns will not be totally random.

In reply to Gerry Windiarto Mohamad Dunda

Re: Question 3.7 on set5

par Christos Sourmpis,

Hello and thanks for your question,

so following the previous steps we need to find the mean value of the expression:

\sum_{\mu\neq1}^Pp_i^1p_i^\mu m^{\mu1}

Although now $m^{\mu1}$ is now deterministic, we consider that when we speak about only one element of the pattern (i am referring to index i) then the situation remains stochastic. So we end up with:

Pr(p_i^1p_i^\mu m^{\mu1} = m^{\mu1}) = Pr(p_i^1p_i^\mu m^{\mu1} = -m^{\mu1}) = 0.5

which leads to E[p_i^1p_i^\mu m^{\mu1}] = 0 and consecutively to :

E[\sum_{\mu \ne1}^Pp_i^1p_i^\mu m^{\mu1}] = 0

Cheers