Final 2016-2017
Let $X_1$, $X_2$ and $X_3$ be random variables with
the following covariance and expected
value tables that miss some of the values.
Following information is given.
• $X_2$ and $X_3$ are independent
• $E(X_1 + X_3) = -1$
• $V(X_2) = 9$
• $\rho_{13} = -0.5$
\begin{tabular}{|c|c|c|c|}
\hline
$Cov(X_i, X_j)$ & $X_1$ & $X_2$ & $X_3$ \\
\hline
$X_1$ & 1 & 0.5 & $k$ \\
\hline
$X_2$ & 0.5 & $m$ & $n$ \\
\hline
$X_3$ & $t$ & $u$ & 4 \\
\hline
\end{tabular}
a. Find the missing values $k$, $m$, $n$, $t$, $u$, $w$.
b. For $Y = 2X_1 + X_2$ calculate $E(Y)$ and
$V(Y)$.
\begin{tabular}{|c|c|c|c|}
\hline
$E(X_i)$ & $X_1$ & $X_2$ & $X_3$ \\
\hline
& $w$ & 0 & -2 \\
\hline
\end{tabular}
