Let s_i be Rademacher variables (+/-1 with P=1/2) and x_i real. I find numerically that E[ | sum_i s_i * x_i |] = max{ | x_i | }. True?

Khinchine's inequality gives me an upper bound on the r.h.s. of (sum_i x_i^2)^(1/2) but I found nothing about the stronger equality being true though the numerics suggest it.

06 June 2013 3,809 2 View