Can some one kindly explain the derivation of normal distribution (univariate) and how it could be approximated for binomial distribution (coin flip problem)? I have searched for hours but could not find any online.
I would like to know how to arrive at below formula and how it helps solve binomial distribution problem:
$f(x) = \dfrac {1}{\sigma \surd{2 \pi}}\text{exp}\Big( \dfrac {1}{2}(\dfrac {x-\mu}{\sigma}\Big)\Big)$
I am at a simple binomial distribution problem:
${\displaystyle P(X=k)={n \choose k}p^{k}(1-p)^{n-k}}$