Probability
The Analysis of Data, volume 1
Important Random Variables: 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}}
$
3.17. Exercises
- The description of the Poisson distribution contains several examples of real world quantities that are approximately distributed Poisson. After reading the motivation behind the Poisson distribution, reflect on why these quantities approximately follow the Poisson distribution.
- The description of the exponential distribution states that it is the only continuous RV with the memoryless property. Can you find a discrete distribution that also has this property?
- Consider the uniform distribution over two disjoint intervals $[a,b] \cup [c,d]$ with $a < b < c < d$. Write down the pdf and cdf of that distribution and derive its expectation and variance.