MATH 351 Homework 03

Pick your favorite discrete distribution that isn't in the Bernoulli family of distributions.
1. Describe why this distribution is discrete.
2. Provide 2 examples of when/why this distribution is used to represent the real world around us. Be sure to mention the parameter(s) of this distribution and the value(s) it/they might take on for your example.
3. Pick one value for each of the parameters for this distribution. Write the theoretical (expectation values for the) mean and variance in terms of these parameters. All the better if you can use/learn $\LaTeX$ to write this answer.
4. Make a converengence plot for the sample mean and the theoretical (expectation value for the) mean that is being estimated.
5. Make a converengence plot for the sample variance and the theoretical (expectation value for the) variance that is being estimated.
6. Plot the (cumulative) distribution function and overlay the sample distribution function / emprical (cumulative) distribution function.
7. Pick a value in the support of your distribution, say $x'$. Make a convergence plot of the (emprical) distribution function $\hat{F}(x')$ and the value of the (cumulative) distribution function that is being estimated, $F(x')$.