Roll two fair six-sided dice, if $Z = max{X,Y}$, then find $E(Z)$ and $V(Z)$.

Question

Roll two fair six-sided dice, and let $X$, $Y$ denote the first and the second numbers.
If $Z = max${$X, Y$}, find $E(Z)$ and $V(Z)$

$P(z)$ for $Z$ being $1, 2, 3, 4, 5, 6 = 1/36, 3/36, 5/36, 7/36, 9/36, 11/36$

$E(Z) = 1*1/36 + 2*3/36 + 3*5/36 + 4*7/36 + 5*9/36 + 6*11/36$
$E(Z) = 4.5$

$V(Z) = (3.5^2+2.5^2+1.5^2+0.5^2+0.5^2+1.5^2) / 6$
$V(Z) = 3.91666666667$

However, the result for $E(Z)$ and $V(Z)$ are wrong...

Answer 1

$V(Z)=\sum P(Z=i) (i-EZ)^{2}$ and $P(Z=i)$ is not $\frac 1 6$.