If we roll a fair die twice and if we let $X$ be the maximum of the two rolls, and $Y$ be the minimum of the two rolls. Then I have to compute $\mathrm{E}[X]$, $\mathrm{Var}[X]$, $\mathrm{E}[Y]$ and $\mathrm{Var}[Y]$.
I thought of the following.
Maximum value to appear in the two rolls $X = \max (\text{roll 1}, \text{roll 2})$ gives $X = \{1,2,3,4,5,6\}$ and
Minimum value to appear in the two rolls $Y = \min (\text{roll 1}, \text{roll 2})$ gives $Y = \{1,2,3,4,5,6\}$.
Any help would be grateful.
What you need are the respective frequencies.
On a total of $36$ possibilities, for the maximum,
$$\begin{matrix}1&2&3&4&5&6\\\hline1&3&5&7&9&11\end {matrix},$$
and for the minimum,
$$\begin{matrix}1&2&3&4&5&6\\\hline11&9&7&5&3&1\end {matrix}.$$
The rest is yours.