Question

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}

          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}

Final 2016-2017
Let X1, X2 and X3 be random variables with
the following covariance and expected
value tables that miss some of the values.
Following information is given.
• X2 and X3 are independent
• E(X1 + X3) = -1
• V(X2) = 9
• ρ13 = -0.5

Cov(Xi, Xj) X1 X2 X3

X1 1 0.5 k

X2 0.5 m n

X3 t u 4

a. Find the missing values k, m, n, t, u, w.
b. For Y = 2X1 + X2 calculate E(Y) and
V(Y).

E(Xi) X1 X2 X3

w 0 -2

Added by Lisa W.

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