SlideShare a Scribd company logo
KME272 Engineering Mathematics 2B 2019 : Assignment 2
Due 5pm September 4th; worth 7.5%. Submit online only.
You have been asked to look at these highly confidential data and have been told certain things about it:
1. Data 1 correspond to a Poisson Process
2. Data 2 correspond to a Binomial Process based on Data 1 values
Your job for $15,000 is to:
1. Find how the Poisson Process gives you the data you saw
2. Find the relationship between Data1 and Data2
3. Simulate data that behave like the data provided
This awful task is helped by your busy statistics friend, who having briefly glanced at the data, makes the following obser-
vations:
1. It’s clearly not a Poisson process, but maybe there’s a Poisson process involved.
2. Start by showing it’s not Poisson.
3. Maybe it’s to do with waiting times.
4. Try fitting some distributions so they have the same mean and variance as those data.
5. You’ll need to use the inverse transform method to simulate from the data.
6. Data2 looks like its values are high when the Data1 values are high - what’s going on with that? Can you plot this
relationship?
1
2
Tasks
1. Why is it “clearly not” Poisson?
(a) Calculate summary statistics for Data1 and use them to argue that the distribution is not a Poisson distribution.
2
(b) Use the method of moments to estimate what the parameter of a Poisson distribution would be to give you
those values. 2
(c) Collate how many values there are in the range 0-4, 5-9, 10-14, etc. and plot the resulting histogram. 2
(d) Use the Chi-square test to determine whether the data fit a Poisson distribution. 2
2. Find a better distribution for Data1:
(a) Show your reasoning for which distribution you choose, and remember, you may need to compare several
distributions. 4
(b) Give all measures of fit you use, including at least the Chi-square measure of fit, calculated as you did in the
question above. You are encouraged to use other measures also. 4
3. You have been told Data2 has some kind of binomial relationship with Data1 values:
(a) Why is it binomial? Provide a justification of why these data fit a binomial distribution. 2
(b) Provide plot(s) to show that Data2 follows a binomial distribution as a function of the values of Data1. 2
4. Simulate data using a spreadsheet or R that have the same characteristics as given in Data2 (which will require you
work out the relationship between Data2 and Data1). In particular, the simulated data should 5
(a) have approximately the same mean and variance as Data2;
(b) have the same upper and lower limits as Data2.
5. Comment on the processes that might be going on. Think about what the assumptions are of the distribution you
have found that you think fits the Data1 and Data2 the best. 5
Style Guide
1. Submit your report as a pdf, and attach all other working (e.g., spreadsheet, R scripts).
2. Write your report in clear English, with correct spelling and grammar.
3. Lay your report out logically and clearly so information is easy to find.
4. Give full working and provide clear, fully labelled plots for your answers in your report.
5. Use full sentences for all answers: instead of writing “mean: 5” write “The mean value was 5” or similar.
Total marks: 30

More Related Content

What's hot

A Fast Content-Based Image Retrieval Method Using Deep Visual Features
A Fast Content-Based Image Retrieval Method Using Deep Visual FeaturesA Fast Content-Based Image Retrieval Method Using Deep Visual Features
A Fast Content-Based Image Retrieval Method Using Deep Visual Features
Hiroki Tanioka
 
Text Analytics
Text AnalyticsText Analytics
Text Analytics
Ajay Ram
 
Poster
PosterPoster
Poster
Sidney Lam
 
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast FiveOzchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
Mannu Amrit
 
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional ApproachExploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
Molham Al-Maleh
 
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
Sri Ambati
 
Levenberg - Marquardt (LM) algorithm_ aghazade
Levenberg - Marquardt (LM) algorithm_ aghazadeLevenberg - Marquardt (LM) algorithm_ aghazade
Levenberg - Marquardt (LM) algorithm_ aghazade
Inistute of Geophysics, Tehran university , Tehran/ iran
 
Dmblog
DmblogDmblog
A Three-Layer Visual Hash Function Using Adler-32
A Three-Layer Visual Hash Function Using Adler-32A Three-Layer Visual Hash Function Using Adler-32
A Three-Layer Visual Hash Function Using Adler-32
Universitas Pembangunan Panca Budi
 

What's hot (9)

A Fast Content-Based Image Retrieval Method Using Deep Visual Features
A Fast Content-Based Image Retrieval Method Using Deep Visual FeaturesA Fast Content-Based Image Retrieval Method Using Deep Visual Features
A Fast Content-Based Image Retrieval Method Using Deep Visual Features
 
Text Analytics
Text AnalyticsText Analytics
Text Analytics
 
Poster
PosterPoster
Poster
 
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast FiveOzchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
Ozchi24 2013 Student Design Challenge Final Presentation, Team Fast Five
 
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional ApproachExploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
Exploiting Big Data in Time Series Forecasting: A Cross-Sectional Approach
 
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
Interpretable Machine Learning Using LIME Framework - Kasia Kulma (PhD), Data...
 
Levenberg - Marquardt (LM) algorithm_ aghazade
Levenberg - Marquardt (LM) algorithm_ aghazadeLevenberg - Marquardt (LM) algorithm_ aghazade
Levenberg - Marquardt (LM) algorithm_ aghazade
 
Dmblog
DmblogDmblog
Dmblog
 
A Three-Layer Visual Hash Function Using Adler-32
A Three-Layer Visual Hash Function Using Adler-32A Three-Layer Visual Hash Function Using Adler-32
A Three-Layer Visual Hash Function Using Adler-32
 

Similar to Assignment2

1 P a g e ME 350 Project 2 Posted February 26.docx
1  P a g e   ME 350 Project 2  Posted February 26.docx1  P a g e   ME 350 Project 2  Posted February 26.docx
1 P a g e ME 350 Project 2 Posted February 26.docx
oswald1horne84988
 
Rubrics & Self Assessments Online Submission
Rubrics & Self Assessments Online SubmissionRubrics & Self Assessments Online Submission
Rubrics & Self Assessments Online Submission
Stephen Taylor
 
Principal components
Principal componentsPrincipal components
Principal components
Hutami Endang
 
BUSI 820Quantitative Researc
BUSI 820Quantitative ResearcBUSI 820Quantitative Researc
BUSI 820Quantitative Researc
VannaSchrader3
 
Chapter 3. Data Preprocessing.ppt
Chapter 3. Data Preprocessing.pptChapter 3. Data Preprocessing.ppt
Chapter 3. Data Preprocessing.ppt
Subrata Kumer Paul
 
Database schema architecture.ppt
Database schema architecture.pptDatabase schema architecture.ppt
Database schema architecture.ppt
ImXaib
 
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
The Statistical and Applied Mathematical Sciences Institute
 
Duplicate Detection of Records in Queries using Clustering
Duplicate Detection of Records in Queries using ClusteringDuplicate Detection of Records in Queries using Clustering
Duplicate Detection of Records in Queries using Clustering
IJORCS
 
Project Deliverable 3 Database and Programming DesignThis ass.docx
Project Deliverable 3 Database and Programming DesignThis ass.docxProject Deliverable 3 Database and Programming DesignThis ass.docx
Project Deliverable 3 Database and Programming DesignThis ass.docx
bfingarjcmc
 
ICDE 2015 - LDV: Light-weight Database Virtualization
ICDE 2015 - LDV: Light-weight Database VirtualizationICDE 2015 - LDV: Light-weight Database Virtualization
ICDE 2015 - LDV: Light-weight Database Virtualization
Boris Glavic
 
Access 05
Access 05Access 05
Access 05
Alexander Babich
 
Enhance The Technique For Searching Dimension Incomplete Databases
Enhance The Technique For Searching Dimension Incomplete DatabasesEnhance The Technique For Searching Dimension Incomplete Databases
Enhance The Technique For Searching Dimension Incomplete Databases
paperpublications3
 
RelateSheets_SSDBM2013_Poster
RelateSheets_SSDBM2013_PosterRelateSheets_SSDBM2013_Poster
RelateSheets_SSDBM2013_Poster
Abdussalam Alawini
 
Instructions 1. Using annual data on GDP from the U.S. Cens.docx
Instructions 1. Using annual data on GDP from the U.S. Cens.docxInstructions 1. Using annual data on GDP from the U.S. Cens.docx
Instructions 1. Using annual data on GDP from the U.S. Cens.docx
dirkrplav
 
Comparative study of Bitmap indexing and B Tree.
Comparative study of Bitmap indexing and B Tree.Comparative study of Bitmap indexing and B Tree.
Comparative study of Bitmap indexing and B Tree.
Sudhanshu Deshmukh
 
Correlation analysis
Correlation analysis Correlation analysis
Correlation analysis
Divyanshu Singh
 
Krupa rm
Krupa rmKrupa rm
Krupa rm
Krupa Mehta
 
Introduction to Data Science With R Notes
Introduction to Data Science With R NotesIntroduction to Data Science With R Notes
Introduction to Data Science With R Notes
LakshmiSarvani6
 
Mba2216 week 11 data analysis part 01
Mba2216 week 11 data analysis part 01Mba2216 week 11 data analysis part 01
Mba2216 week 11 data analysis part 01
Stephen Ong
 
Upstate CSCI 525 Data Mining Chapter 3
Upstate CSCI 525 Data Mining Chapter 3Upstate CSCI 525 Data Mining Chapter 3
Upstate CSCI 525 Data Mining Chapter 3
DanWooster1
 

Similar to Assignment2 (20)

1 P a g e ME 350 Project 2 Posted February 26.docx
1  P a g e   ME 350 Project 2  Posted February 26.docx1  P a g e   ME 350 Project 2  Posted February 26.docx
1 P a g e ME 350 Project 2 Posted February 26.docx
 
Rubrics & Self Assessments Online Submission
Rubrics & Self Assessments Online SubmissionRubrics & Self Assessments Online Submission
Rubrics & Self Assessments Online Submission
 
Principal components
Principal componentsPrincipal components
Principal components
 
BUSI 820Quantitative Researc
BUSI 820Quantitative ResearcBUSI 820Quantitative Researc
BUSI 820Quantitative Researc
 
Chapter 3. Data Preprocessing.ppt
Chapter 3. Data Preprocessing.pptChapter 3. Data Preprocessing.ppt
Chapter 3. Data Preprocessing.ppt
 
Database schema architecture.ppt
Database schema architecture.pptDatabase schema architecture.ppt
Database schema architecture.ppt
 
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentati...
 
Duplicate Detection of Records in Queries using Clustering
Duplicate Detection of Records in Queries using ClusteringDuplicate Detection of Records in Queries using Clustering
Duplicate Detection of Records in Queries using Clustering
 
Project Deliverable 3 Database and Programming DesignThis ass.docx
Project Deliverable 3 Database and Programming DesignThis ass.docxProject Deliverable 3 Database and Programming DesignThis ass.docx
Project Deliverable 3 Database and Programming DesignThis ass.docx
 
ICDE 2015 - LDV: Light-weight Database Virtualization
ICDE 2015 - LDV: Light-weight Database VirtualizationICDE 2015 - LDV: Light-weight Database Virtualization
ICDE 2015 - LDV: Light-weight Database Virtualization
 
Access 05
Access 05Access 05
Access 05
 
Enhance The Technique For Searching Dimension Incomplete Databases
Enhance The Technique For Searching Dimension Incomplete DatabasesEnhance The Technique For Searching Dimension Incomplete Databases
Enhance The Technique For Searching Dimension Incomplete Databases
 
RelateSheets_SSDBM2013_Poster
RelateSheets_SSDBM2013_PosterRelateSheets_SSDBM2013_Poster
RelateSheets_SSDBM2013_Poster
 
Instructions 1. Using annual data on GDP from the U.S. Cens.docx
Instructions 1. Using annual data on GDP from the U.S. Cens.docxInstructions 1. Using annual data on GDP from the U.S. Cens.docx
Instructions 1. Using annual data on GDP from the U.S. Cens.docx
 
Comparative study of Bitmap indexing and B Tree.
Comparative study of Bitmap indexing and B Tree.Comparative study of Bitmap indexing and B Tree.
Comparative study of Bitmap indexing and B Tree.
 
Correlation analysis
Correlation analysis Correlation analysis
Correlation analysis
 
Krupa rm
Krupa rmKrupa rm
Krupa rm
 
Introduction to Data Science With R Notes
Introduction to Data Science With R NotesIntroduction to Data Science With R Notes
Introduction to Data Science With R Notes
 
Mba2216 week 11 data analysis part 01
Mba2216 week 11 data analysis part 01Mba2216 week 11 data analysis part 01
Mba2216 week 11 data analysis part 01
 
Upstate CSCI 525 Data Mining Chapter 3
Upstate CSCI 525 Data Mining Chapter 3Upstate CSCI 525 Data Mining Chapter 3
Upstate CSCI 525 Data Mining Chapter 3
 

Recently uploaded

Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s DholeraTata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
Avirahi City Dholera
 
Creative Web Design Company in Singapore
Creative Web Design Company in SingaporeCreative Web Design Company in Singapore
Creative Web Design Company in Singapore
techboxsqauremedia
 
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
bosssp10
 
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdfThe 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
thesiliconleaders
 
-- June 2024 is National Volunteer Month --
-- June 2024 is National Volunteer Month ---- June 2024 is National Volunteer Month --
-- June 2024 is National Volunteer Month --
NZSG
 
2024-6-01-IMPACTSilver-Corp-Presentation.pdf
2024-6-01-IMPACTSilver-Corp-Presentation.pdf2024-6-01-IMPACTSilver-Corp-Presentation.pdf
2024-6-01-IMPACTSilver-Corp-Presentation.pdf
hartfordclub1
 
Authentically Social Presented by Corey Perlman
Authentically Social Presented by Corey PerlmanAuthentically Social Presented by Corey Perlman
Authentically Social Presented by Corey Perlman
Corey Perlman, Social Media Speaker and Consultant
 
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta MatkaDpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
 
ikea_woodgreen_petscharity_cat-alogue_digital.pdf
ikea_woodgreen_petscharity_cat-alogue_digital.pdfikea_woodgreen_petscharity_cat-alogue_digital.pdf
ikea_woodgreen_petscharity_cat-alogue_digital.pdf
agatadrynko
 
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
Lviv Startup Club
 
buy old yahoo accounts buy yahoo accounts
buy old yahoo accounts buy yahoo accountsbuy old yahoo accounts buy yahoo accounts
buy old yahoo accounts buy yahoo accounts
Susan Laney
 
2022 Vintage Roman Numerals Men Rings
2022 Vintage Roman  Numerals  Men  Rings2022 Vintage Roman  Numerals  Men  Rings
2022 Vintage Roman Numerals Men Rings
aragme
 
Lundin Gold Corporate Presentation - June 2024
Lundin Gold Corporate Presentation - June 2024Lundin Gold Corporate Presentation - June 2024
Lundin Gold Corporate Presentation - June 2024
Adnet Communications
 
Part 2 Deep Dive: Navigating the 2024 Slowdown
Part 2 Deep Dive: Navigating the 2024 SlowdownPart 2 Deep Dive: Navigating the 2024 Slowdown
Part 2 Deep Dive: Navigating the 2024 Slowdown
jeffkluth1
 
Authentically Social by Corey Perlman - EO Puerto Rico
Authentically Social by Corey Perlman - EO Puerto RicoAuthentically Social by Corey Perlman - EO Puerto Rico
Authentically Social by Corey Perlman - EO Puerto Rico
Corey Perlman, Social Media Speaker and Consultant
 
Creative Web Design Company in Singapore
Creative Web Design Company in SingaporeCreative Web Design Company in Singapore
Creative Web Design Company in Singapore
techboxsqauremedia
 
Best Forex Brokers Comparison in INDIA 2024
Best Forex Brokers Comparison in INDIA 2024Best Forex Brokers Comparison in INDIA 2024
Best Forex Brokers Comparison in INDIA 2024
Top Forex Brokers Review
 
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
ABHILASH DUTTA
 
Best practices for project execution and delivery
Best practices for project execution and deliveryBest practices for project execution and delivery
Best practices for project execution and delivery
CLIVE MINCHIN
 
Training my puppy and implementation in this story
Training my puppy and implementation in this storyTraining my puppy and implementation in this story
Training my puppy and implementation in this story
WilliamRodrigues148
 

Recently uploaded (20)

Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s DholeraTata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
Tata Group Dials Taiwan for Its Chipmaking Ambition in Gujarat’s Dholera
 
Creative Web Design Company in Singapore
Creative Web Design Company in SingaporeCreative Web Design Company in Singapore
Creative Web Design Company in Singapore
 
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
Call 8867766396 Satta Matka Dpboss Matka Guessing Satta batta Matka 420 Satta...
 
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdfThe 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdf
 
-- June 2024 is National Volunteer Month --
-- June 2024 is National Volunteer Month ---- June 2024 is National Volunteer Month --
-- June 2024 is National Volunteer Month --
 
2024-6-01-IMPACTSilver-Corp-Presentation.pdf
2024-6-01-IMPACTSilver-Corp-Presentation.pdf2024-6-01-IMPACTSilver-Corp-Presentation.pdf
2024-6-01-IMPACTSilver-Corp-Presentation.pdf
 
Authentically Social Presented by Corey Perlman
Authentically Social Presented by Corey PerlmanAuthentically Social Presented by Corey Perlman
Authentically Social Presented by Corey Perlman
 
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta MatkaDpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
Dpboss Matka Guessing Satta Matta Matka Kalyan Chart Satta Matka
 
ikea_woodgreen_petscharity_cat-alogue_digital.pdf
ikea_woodgreen_petscharity_cat-alogue_digital.pdfikea_woodgreen_petscharity_cat-alogue_digital.pdf
ikea_woodgreen_petscharity_cat-alogue_digital.pdf
 
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
Evgen Osmak: Methods of key project parameters estimation: from the shaman-in...
 
buy old yahoo accounts buy yahoo accounts
buy old yahoo accounts buy yahoo accountsbuy old yahoo accounts buy yahoo accounts
buy old yahoo accounts buy yahoo accounts
 
2022 Vintage Roman Numerals Men Rings
2022 Vintage Roman  Numerals  Men  Rings2022 Vintage Roman  Numerals  Men  Rings
2022 Vintage Roman Numerals Men Rings
 
Lundin Gold Corporate Presentation - June 2024
Lundin Gold Corporate Presentation - June 2024Lundin Gold Corporate Presentation - June 2024
Lundin Gold Corporate Presentation - June 2024
 
Part 2 Deep Dive: Navigating the 2024 Slowdown
Part 2 Deep Dive: Navigating the 2024 SlowdownPart 2 Deep Dive: Navigating the 2024 Slowdown
Part 2 Deep Dive: Navigating the 2024 Slowdown
 
Authentically Social by Corey Perlman - EO Puerto Rico
Authentically Social by Corey Perlman - EO Puerto RicoAuthentically Social by Corey Perlman - EO Puerto Rico
Authentically Social by Corey Perlman - EO Puerto Rico
 
Creative Web Design Company in Singapore
Creative Web Design Company in SingaporeCreative Web Design Company in Singapore
Creative Web Design Company in Singapore
 
Best Forex Brokers Comparison in INDIA 2024
Best Forex Brokers Comparison in INDIA 2024Best Forex Brokers Comparison in INDIA 2024
Best Forex Brokers Comparison in INDIA 2024
 
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
The Evolution and Impact of OTT Platforms: A Deep Dive into the Future of Ent...
 
Best practices for project execution and delivery
Best practices for project execution and deliveryBest practices for project execution and delivery
Best practices for project execution and delivery
 
Training my puppy and implementation in this story
Training my puppy and implementation in this storyTraining my puppy and implementation in this story
Training my puppy and implementation in this story
 

Assignment2

  • 1. KME272 Engineering Mathematics 2B 2019 : Assignment 2 Due 5pm September 4th; worth 7.5%. Submit online only. You have been asked to look at these highly confidential data and have been told certain things about it: 1. Data 1 correspond to a Poisson Process 2. Data 2 correspond to a Binomial Process based on Data 1 values Your job for $15,000 is to: 1. Find how the Poisson Process gives you the data you saw 2. Find the relationship between Data1 and Data2 3. Simulate data that behave like the data provided This awful task is helped by your busy statistics friend, who having briefly glanced at the data, makes the following obser- vations: 1. It’s clearly not a Poisson process, but maybe there’s a Poisson process involved. 2. Start by showing it’s not Poisson. 3. Maybe it’s to do with waiting times. 4. Try fitting some distributions so they have the same mean and variance as those data. 5. You’ll need to use the inverse transform method to simulate from the data. 6. Data2 looks like its values are high when the Data1 values are high - what’s going on with that? Can you plot this relationship? 1
  • 2. 2 Tasks 1. Why is it “clearly not” Poisson? (a) Calculate summary statistics for Data1 and use them to argue that the distribution is not a Poisson distribution. 2 (b) Use the method of moments to estimate what the parameter of a Poisson distribution would be to give you those values. 2 (c) Collate how many values there are in the range 0-4, 5-9, 10-14, etc. and plot the resulting histogram. 2 (d) Use the Chi-square test to determine whether the data fit a Poisson distribution. 2 2. Find a better distribution for Data1: (a) Show your reasoning for which distribution you choose, and remember, you may need to compare several distributions. 4 (b) Give all measures of fit you use, including at least the Chi-square measure of fit, calculated as you did in the question above. You are encouraged to use other measures also. 4 3. You have been told Data2 has some kind of binomial relationship with Data1 values: (a) Why is it binomial? Provide a justification of why these data fit a binomial distribution. 2 (b) Provide plot(s) to show that Data2 follows a binomial distribution as a function of the values of Data1. 2 4. Simulate data using a spreadsheet or R that have the same characteristics as given in Data2 (which will require you work out the relationship between Data2 and Data1). In particular, the simulated data should 5 (a) have approximately the same mean and variance as Data2; (b) have the same upper and lower limits as Data2. 5. Comment on the processes that might be going on. Think about what the assumptions are of the distribution you have found that you think fits the Data1 and Data2 the best. 5 Style Guide 1. Submit your report as a pdf, and attach all other working (e.g., spreadsheet, R scripts). 2. Write your report in clear English, with correct spelling and grammar. 3. Lay your report out logically and clearly so information is easy to find. 4. Give full working and provide clear, fully labelled plots for your answers in your report. 5. Use full sentences for all answers: instead of writing “mean: 5” write “The mean value was 5” or similar. Total marks: 30