In Bishop's book (Pattern recognition and machine learning, pag 122) there is an unclear passage for me in deriving certain formulas:
$E[K/N] = P$ and $var[K/N] = P(1-P)$
Considering binomial probability
$P(x=x) = \binom{N}{x} P^{x} \cdot (1 - P)^{(N-x)}$
I know that the expected value and variance is given by:
$E(X) = N \cdot x$
$var(X) = N \cdot x \cdot (1-x)$
As a first thing since Bishop refers to the fraction of points that fall in the bin, i.e., K/N, I would be tempted to substitute N for K/N, however, there are some steps (perhaps algebraic) that I am missing.
