Two-dimensional Gaussian Random Variables

© 2021 Institute for Communications Engineering, Technical University of Munich
Authors: Carolin Mirschina & Tasnad Kernetzky
$\sigma _X =$
$1.00$
$\sigma _Y =$
$0.50$
$\rho _{XY}=$
$0.70$
$\rm{PDF}$: $z=f_{XY}(x,y)$
$\rm{CDF}$: $z=F_{XY}(x,y)$
$\rm{Show \ contour \ lines}$
$ \rm{1D}$-$\rm{PDF}$
$f_X(x)$
$f_Y(y)$
Exercises

    * Select the number  $(1,\ 2$, ... $)$  of the task to be processed.  The number "0" corresponds to a "Reset":  Setting as at the program start.
    * A task description is displayed.  Parameter values are adjusted.  Solution after pressing "Sample solution". 
    * In the task description, we use  $\rho$  instead of  $\rho_{XY}$.
    * For the one-dimensional Gaussian PDF holds:  $f_{X}(x) = \sqrt{1/(2\pi \cdot \sigma_X^2)} \cdot {\rm e}^{-x^2/(2 \hspace{0.05cm}\cdot \hspace{0.05cm} \sigma_X^2)}$.