Create a bivariate normal distribution with $200$ samples whose mean is

$u=[0,1]$ and the covariance

matrix is

$=\left[\begin{array}{cc}1& 0\mathrm{.}0\\ 0\mathrm{.}0& 2.\end{array}\right]$

$[10]$ Plot the PDF of the samples.

$[10]$ Plot the PDF of the first variable and the second variable.

$[10]$ Calculate the correlation between the first $x$ and the second random variable $Y,$ and show their

scattering plot.

$[10]$ Define a new random variable $Z$ as $Z=x+Y.$ What is the $E[Z]$ and VAR$[Z].$

$[10]$ Plot the PDF of $Z.$

$[10]$ Calculate the correlation and covariance between the first variable $x$ and the new random variable

$Z,$ and show their scattering plot.

$[10]$ Interprept the calculated correlations and covariances between $x$&$Y$ and $x$&$Z.$ t and $$ equal to zero $(0)$