About This Assignment

This mini-project covers aspects of a discrete distribution from Chapter 4 along with related theory. 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.

Name of Problem

Introduction

The Poisson distribution can be used to model many data sets in science where an average number of events occurs in a particular unit of time/space/volume etc.

The characteristics of a Poisson distribution are given in the text on page 169. In this mini-project, you will need to calculate some moments using first principles.

Calculation

Answer using an RMD document - you may write the answers neatly on paper, take a picture, and place it in RMD using ![](file name){}

Find where . Use the definition of Expected value only,
- Derive the formula
- Now calculate the numerical answer when $LaTeX: \lambda = 4$
Derive the formula for the Poisson MGF - show all working.
Use the MGF you derived to find the formula for
Knit to HTML and upload after answering the quiz

You may need the following Taylor series result:

$LaTeX: \sum_{y=0}^\infty\frac{\lambda^y}{y!} = e^{\lambda}$