Question 3.7 on set5

Re: Question 3.7 on set5

by Christos Sourmpis -
Number of replies: 0

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