In a game of roulette if you bet \$1 you either win \$35 with a probability of 1/38 or loose \$1 with a probability of 37/38. Thus I calculate the chance of winning on a single play as $E(W)=35/38 -37/38 = -1/19$
It has been explained to me that we calculate Variance using
$Var(f(X))=E[f(X)^2]-E[f(X)]^2$
In our case $f(X)=W$
and I am told that $E[W^2]=35^2\frac{1}{38}+(-1)^2 \frac{37}{38}$
Why can we not use $E[W^2]=(-1/19)^2$ ?