A random variable $X$ is number of boys out of $n$ children. Calculate $\operatorname{Var}(2X-n)$ 
Let a random variable $X$ be the number of boys out of $n$ children. The probability to have a boy or a girl is $0.5$. Calculate $V(2X-n)$.

I know that $Var(2X-n)=4V(X)$.
$\mathbb{P}(X=k)={1\over 2^n}\binom{n}{k}$. Thus $\mathbb{E}(X)=\sum_{i=1}^n{1\over 2^n}\binom{n}{k}\cdot k$, and $\mathbb{E}(X^2)=\sum_{i=1}^n{1\over 2^n}\binom{n}{k}\cdot k^2$. I'm not sure how to keep on.

$$V(2X - n) = V(2X) = 2^2V(X)$$
$X$ follows a binomial distribution with $n$ trials and $p=0.5$, which has $V(X) = np(1-p)$
$$V(2X - n) = 4np(1-p)$$
