About This Assignment

In this mini-project you will need to derive the MGF for an exponential and then find the distribution of Y = 2X. You will be asked to show your work on the next assignment page by submitting an HTML file.

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.

Name of Problem

Introduction

An exponential distribution is defined as a Gamma with alpha = 1. Suppose $LaTeX: Y \sim Exp(\beta)$ and further that LaTeX: L = 2Y .

Calculation

Using an RMD document do the following:

Prove $LaTeX: M_Y(t) = \frac{1}{1-\beta t}$ use latex/picture
Find the expression for use latex/picture
Find the ratio of the variances $LaTeX: \frac{\sigma_Y^2}{\sigma_L^2}$ use latex/picture

Knit to HTML.

Now answer the question below