\\\\(
\nonumber
\newcommand{\bevisslut}{$\blacksquare$}
\newenvironment{matr}[1]{\hspace{-.8mm}\begin{bmatrix}\hspace{-1mm}\begin{array}{#1}}{\end{array}\hspace{-1mm}\end{bmatrix}\hspace{-.8mm}}
\newcommand{\transp}{\hspace{-.6mm}^{\top}}
\newcommand{\maengde}[2]{\left\lbrace \hspace{-1mm} \begin{array}{c|c} #1 & #2 \end{array} \hspace{-1mm} \right\rbrace}
\newenvironment{eqnalign}[1]{\begin{equation}\begin{array}{#1}}{\end{array}\end{equation}}
\newcommand{\eqnl}{}
\newcommand{\matind}[3]{{_\mathrm{#1}\mathbf{#2}_\mathrm{#3}}}
\newcommand{\vekind}[2]{{_\mathrm{#1}\mathbf{#2}}}
\newcommand{\jac}[2]{{\mathrm{Jacobi}_\mathbf{#1} (#2)}}
\newcommand{\diver}[2]{{\mathrm{div}\mathbf{#1} (#2)}}
\newcommand{\rot}[1]{{\mathbf{rot}\mathbf{(#1)}}}
\newcommand{\am}{\mathrm{am}}
\newcommand{\gm}{\mathrm{gm}}
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\newcommand{\Span}{\mathrm{span}}
\newcommand{\mU}{\mathbf{U}}
\newcommand{\mA}{\mathbf{A}}
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\newcommand{\mE}{\mathbf{E}}
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\newcommand{\mK}{\mathbf{K}}
\newcommand{\mI}{\mathbf{I}}
\newcommand{\mM}{\mathbf{M}}
\newcommand{\mN}{\mathbf{N}}
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\\\\)
Download the script
exercise_simulationexamples.R and
run the different parts, while answering the questions below.
- Run the code: For the first part, try changing the mean and
covariance, and:
- make some observations about how the joint pdf
is affected.
- Can you make the calculations break down? (i.e.\ can
$\Sigma$ be set, such that the calculations are not possible).
-
Consider the quesion: Will a “straight slice” through the bi-variate
normal distribution, also be a normal distribution?
-
First time there are two times ‘??’: Can you make the code that
calculates the mean and covariance of the transformed random vector,
such that it matches the mean and variance of simulated values, approximately.
-
Second time there are two times ‘??’: Again, make the code calculating
the mean and variance of the linear model output. Can you make it
match the mean and variance simulated values, approximately.
- A solution can be found here
exercise_simulationexamples_solution.R
