Combine independent random variables and normal distributions
Give exact values except where a probability is explicitly requested to four decimal places. In N(μ,σ²), the second parameter is the variance
X and Y are independent, with the following means and variances
\[E(X)=3,\quad E(Y)=-2,\quad \operatorname{Var}(X)=1,\quad \operatorname{Var}(Y)=1,\quad W=(1)X+(-1)Y+(3)\]