Let X_{1}, X_{2}, X_{3},
..., X_{n} be random variables
corresponding to n Bernoulli trials (experiments), and let Z be the
random variable:
Z = å_{i=1,n} X_{i}
The distribution of Z is the binomial
æ ænöp^{z}(1-p)^{(n-z)}
ç ç ÷
ç èzø
f(z) = ç z=0,1,2,3,...,n
ç
è 0 otherwise
Where: E(Z) = E[X_{1} + X_{2} + ... + X_{n}] =
E(X_{1}) + E(X_{2}) + ... + E(X_{n}) =
p + p + ... + p = np
VAR(Z) = VAR[X_{1} + X_{2} + ... + X_{n}] =
VAR(X_{1}) + VAR(X_{2}) + ... + VAR(X_{n}) =
p(1 - p) + p(1 - p) + ... + p(1 - p) = np(1 - p)