MATH 351 Homework 04

Use the Exponential Distribution throughout this assignment.
1. Describe why this distribution is continuous.
2. Provide 2 examples of when/why this distribution is used to represent the real world around us. Be sure to mention the parameter of this distribution and the value it might take on for your example.
3. Pick one value for the parameter for this distribution. Write the theoretical (expectation values for the) mean and variance in terms of this parameter. 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. Make a convergence plot for a meaningful probability, with respect to your one of your examples above.
7. Plot the (cumulative) distribution function and overlay the sample distribution function / emprical (cumulative) distribution function.