Week 3

This week, we will review basic properties of MGFs and introduce markdown and R/QMDs.
Published

September 5, 2022

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