Negative Variance I have two independent variables $X$ and $Y$.
$W=X-Y$ when $X\sim \mbox{Bernoulli}\left(1/2\right)$ and $Y\sim N(0,1)$. This puts $\operatorname{Var}(x)=1/4$ and $\operatorname{Var}(Y)=1$, but I have to be misunderstanding something because if $\operatorname{Var}(W)=\operatorname{Var}(X)-\operatorname{Var}(Y)$ then the $\operatorname{Var}(W)$ is negative, which makes no sense. 
What am I missing?

If $U$ and $V$ are independent, then $\text{Var}(aU+bV)=a^2\text{Var}(U)+b^2\text{Var}(V)$.  In our case, the variance of $X-Y$, that is, of $(1)X+(-1)Y$, is the variance of $X$ plus the variance of $Y$.
