Week 3
Learning Outcomes
Wednesday
Moment Generating Functions Properties
Introduction to Q/RMD
Reading
| Day | Reading |
|---|---|
| Monday’s Lecture | Holiday |
| Wednesday’s Lecture | MMS: 4.2 |
Homework
Homework 2 can be found here: https://m453.inqs.info/hws/hw2.html
It is due 9/16/2022 at 11:59PM.
Important Concepts
MGF Properties
Linearity
Let \(X\) follow a distribution \(f\), with the an MGF \(M_X(t)\), the MGF of \(Y=aX+b\) is given as
\[ M_Y(t) = e^{tb}M_X(at) \]
Let \(X\) and \(Y\) be two random variables with MGFs \(M_X(t)\) and \(M_Y(t)\), respectively, and are independent. The MGF of \(U=X-Y\)
\[ M_U(t) = M_X(t)M_Y(-t) \]
Uniqueness
Let \(X\) and \(Y\) have the following distributions \(F_X(x)\) and \(F_Y(y)\) and MGFs \(M_X(t)\) and \(M_Y(t)\), respectively. \(X\) and \(Y\) have the same distribution \(F_X(x)=F_Y(y)\) if and only if \(M_X(t)=M_Y(t)\).
Rmarkdown and Quarto
Rmarkdown is a documentation system that allows you to embed R code and/or output to you document. Additionally, Rmarkdown allows you to export the document to different formats, such as html, word, or pdf.
Quarto is the next generation of Rmarkdown that expands it’s capabilities to more formats and different languages. Additionally, Quarto allows to be utilized in different IDE’s such as RStudio and Visual Code.
Resources
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| Lecture | Slides | Videos |
|---|---|---|
| Monday | N/A | N/A |
| Wednesday | Slides | Video |