Probability
The Analysis of Data, volume 1
Random Vectors: Exercises
$
\def\P{\mathsf{\sf P}}
\def\E{\mathsf{\sf E}}
\def\Var{\mathsf{\sf Var}}
\def\Cov{\mathsf{\sf Cov}}
\def\std{\mathsf{\sf std}}
\def\Cor{\mathsf{\sf Cor}}
\def\R{\mathbb{R}}
\def\c{\,|\,}
\def\bb{\boldsymbol}
\def\diag{\mathsf{\sf diag}}
\def\defeq{\stackrel{\tiny\text{def}}{=}}
$
4.11. Exercises
- Consider two independent discrete RVs $X,Y$ that are uniform over $\{1,2,3,4\}$. Derive the pmf of the RV $X+Y$ using the convolution technique.
- Repeat (1) for $X-Y$.
- Specify formally a pair of RVs $X,Y$ for which $\Cov(X,Y)=0$.