  We calculate the so-called Rademacher's Grand Lebesgue Space norm for a
centered (shifted) indicator (Bernoulli's, binary) random variable.
  This norm is optimal for the centered and bounded random variables (r.v.).
Using this result we derive a very simple bilateral sharp exponential tail
estimates for sums of these variables, not necessary to be identical
distributed, under non-standard norming, and give some examples to show the
exactness of our estimates.
