a) For a Uniform distribution $$Y \sim \operatorname{U}(\var{lower},\var{upper})$$ we have:

$\displaystyle \operatorname{E}[Y] = \simplify[!collectNumbers]{({lower}+{upper})/2}=\var{ans1}$

$\displaystyle \operatorname{Var}(Y) =\simplify[basic,!collectNumbers,!noleadingminus]{({upper}-{lower})^2/12}=\frac{\var{upper-lower}^2}{12}=\var{ans2}$ to 3 decimal places.

b)

$\displaystyle P(Y \le \var{c})=\simplify[basic,!collectNumbers,!noleadingminus]{({c} -{lower})/({upper}-{lower})}=\var{ans3}$ to 3 decimal places.

c) The CDF for a uniform distribution $Y$ on the interval $a \le y \le b$ is given by:

$$F_Y(y) = \begin{cases} 0 & y \lt a \\ \frac{y-a}{b-a} & a \le y \le b, \\ 1 & y \gt b. \end{cases}$$

 Hence in this case we have:

$$F_Y(y) = \simplify[basic]{(y-{lower})/({upper-lower})}$$ for $\var{lower}\le y \le \var{upper}$

d) Using the CDF we have:

$$\begin{eqnarray}P(\var{d} \lt Y \lt \var{f})&=&F_Y(\var{f})-F_Y(\var{d})\\&=&   \simplify[basic]{({f}-{lower})/({upper-lower})- ({d}-{lower})/({upper-lower})}\\&=&\var{ans4}\end{eqnarray}$$

to 3 decimal places.