Derivation of the Mean and Variance of the Binomial Distribution

Students often struggle with the algebraic expansion of the expectation sum. The most efficient path is using the identity

k \binom{n}{k} = n \binom{n-1}{k-1}

, which reduces the complexity of the summation to a standard Binomial expansion of power

n-1

rather than brute-force expansion.

Institutional Reference: Applied Statistics