Variance of Binomial Distribution/Proof 3

Proof
From Bernoulli Process as Binomial Distribution, we see that $X$ as defined here is the sum of the discrete random variables that model the Bernoulli distribution.

Each of the Bernoulli trials is independent of each other.

Hence we can use Sums of Variances of Independent Trials.

The Variance of Bernoulli Distribution is $p \left({1 - p}\right)$.

Thus the variance of $B \left({n, p}\right)$ is $n p \left({1 - p}\right)$.