About This Assignment

This mini-project covers an application of theory related to continuous random variables. You will be tasked with answering a challenging word problem. 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.

MGF and continuous RV

Introduction

A continuous random variable must take a distribution that is defined over the complete real number line. You will need to learn the mathematical skills of applying definitions in a rigorous fashion to any well-defined continuous random variable.

Calculation

Consider the following random variable Y with the density:

$LaTeX: f(y) = \left\{\matrix{e^y,\; y<0\\ 0,\; else} \right .$

Using an RMD document derive the following:

the MGF for Y, please use Latex
$LaTeX: \mu_Y$ using first principles (Do not use the MGF) Hints: Integration by parts, L' Hopitals rule, also use a picture of your working in RMD
$LaTeX: \mu_Y \; and\; \sigma_Y^2$ using the MGF of part 1. Hint: You should get the same first-moment answer as part 2. Please use a picture for your work in RMD.

Now that you have done this, please answer the three quiz questions.