%Fall 01 Practice problems 12

\begin{problem}

Let $X$ be a random variable whose value is an observation
drawn uniformly at random from the set
$\{-n,-n+1,\ldots,-2,-1,0,1,2,\ldots,n-1,n\}$.
Let $Y = X^2$.  Then which of the following are true:
\begin{problemparts}
\problempart
$\expect{X}=0$
\solution{True}
\problempart
$\expect{Y}=0$
\solution{False}
\problempart
$\expect{Y}>\expect{X}$
\solution{True}
\problempart
$\expect{X+Y}=\expect{X}+\expect{Y}$
\solution{True}
\problempart
$\expect{XY}=\expect{X}\expect{Y}$
\solution{True}
\problempart
$X, Y$ are independent variables.
\solution{False}
\problempart
$\variance{X}=0$
\solution{False}
\problempart
$\variance{Y}=0$
\solution{False}
\problempart
$\variance{Y}>\variance{X}$
\solution{True}
\problempart
$\variance{X+Y}=\variance{X}+\variance{Y}$
\solution{False}
\problempart
$\variance{XY}=\variance{X}\variance{Y}$
\solution{False}
\end{problemparts}

\end{problem}
