About This Assignment

This mini-project will require you to use your knowledge of bivariate random variables and their distributions to find the cumulative distribution function and density of a ratio of two random variables. You will be asked to show your work on the next assignment page by submitting HTML.

Format: numeric answer "quiz"
Time limit: none
Number of attempts: 3 total

Academic Integrity

Getting help from your peers is not permitted.
Collaborating, or completing the quiz with others in the class, is not permitted.
Copying or reusing previous work is not permitted.
Open-book research for the quiz is permitted and encouraged.

The ratio problem

Introduction

Suppose that X and Y are independent and:

$LaTeX: f_X(x) = \alpha e^{-\alpha x}, \; x> 0\\ f_Y(y) = \beta e^{-\beta y}, \; y> 0$

Further:

$LaTeX: Z = \frac{X}{Y}$

Calculation

Your job will be to find the following:

The cumulative distribution function of Z, .
The probability density function of Z, .
In both cases detail the domain over which the functions are defined.

Use an RMD document and give the two functions in Latex with the work a picture of your handwriting included using![](){} then knit to HTML.

Now answer the quiz question.