Math 422-01 (Spring 2020)
Mathematical Statistics, Spring 2020, Math 422 - 01
You will want to check back here regularly as I may post a variety of course materials or links to various resources.
Syllabus
Video Lectures:
Chapter 14:
14.1-2 | video / R code text / pdf of notes
You should review some topics from chapters 3 and 4:
joint distributions, marginal and conditional distributions, and conditional expectations,
specifically sections 3.5,6,7 Multivariate, marginal and conditional distributions,
and 4.6 covariance, 4.8 conditional expectation
See my Math 421 review notes on that course page.
14.3 | Least squares regression - video / Rcode / dataset / jpg of notes
14.4-5 | Normal correlation and regression - video / Desmos plot / R code / jpg of notes / R code used to calc cond mean and var
Chapter 15:
One-way ANOVA | video / pdf of notes / R code / state covid data - metadata
Additional topic:
Rejection sampling | video / pdf of notes / R code
FREE Digital textbook access:
For free access to digital textbooks (good through May 25, 2020) sign up for a VitalSource account. You should be able to access most texts from most publishers. Here is more information: VitalSource Helps (go about 2/3 down to pink band on page). Sign up for a VitalSource Bookshelf account, and you can either download the local software or use a webrowser to view digital textbooks. There are also apps for various other devices. Bookshelf is their app for requesting access to and viewing digital testbooks.
I have successfully used VItalSource on both my laptop and phone.
Disclaimer: I haven't tested this free student access and do not know the exact procedure for gaining access to you textbooks digitally. It should NOT require any kind of payment information. Presumably, just create a Bookshelf account and there should be a way to search for your textbook and request access through that app.
Scanning work for turning in:
When turning in work via email, please convert it into a single high resolution pdf document (per assignment). This will make it easiest for me to keep everything organized and to write comments on the work to send back to you.
CamScanner is an app that I use to scan from phone to pdf. You can take multiple pictures and it will output a single pdf. It's available for both Android and iPhone. I am sure there are many similar apps. This one leaves a watermark with the free version. That's fine.
If you have a local scanner, that should work too. I prefer 300dpi and color, but 150dpi may suffice. Please check your pdf document so that the work is legible. Sometimes small writing or light writing (such as soft pencil) doesn't scan well. I suggest using blue or black ink or a sufficiently dark pencil for your written work. You could even try photos of boardwork, but make sure to organize it into a single document (per assignment).
Homework:
HW 1: Ch. 8 # 35,40,41,42,46,77,82
HW 2: Ch. 10 # 1,2,5,6,13,15,35,50,52,61,80
HW 3: Ch. 11 # 5 (just think about it and make an argument, no rigorous computations needed),
6 (the e is not the natural exponential e, maybe use a different letter if you like),
11 (hint: square and solve), 12, 19, 24, 36, 40, 53, 57
HW 4: Ch. 12 # 30,35,36,39,44
Ch. 13 # 19, 20, (25,26), (30,31,32), 44 (paired t-test), 49 (single variance),
63 (single proportion), 73 (multi-proportion), 76 (independence test),
81 (goodness of fit for Poisson)
HW 5: pdf - Due 4/15
GDP-CPI data
COVID-19 state data
video of my own exploration of the data using R
R code I used in the video
HW 6: pdf - Due Weds 5/6,
Use the state covid data linked above with the video.
See the metadata to understand what each column is.
Since the Date is in numerical format, you'll need to convert it to a factor with:
as.factor(d$Date) -> d$Date
Other Assignments:
Quiz 1: Due Wednesday 2/19. (Monday is a holiday)
Exam 1: Due Friday, 3/27. Turn in by sending a pdf via email.
Final Exam: Due Friday, 5/8. covid19 & population density dataset Submit via email as a single scanned pdf.
Review materials:
Here I will post additional review materials such as formula sheets or problems/solutions.
Course notes:
You are advised to acquire a copy of the textbook. I will provide some of my own notes as well in order to supplement the text.
See my Math 421 course page as well for some review materials.
You are free to look at my Summer 2019 Math 321 course page where I have the most recent complete version of my own probability/statistics notes. If I am teaching Math 321 in the current semester, you should check on that course's website for updated notes. These notes are not comprehensive over what Math 421/422 sequence covers, but you might find them helpful. Also, there are many review problems with solutions on that course page as well. Chapters 2,3, and 4 are most relevant for Math 421. Chapters 5,6,7 and 8 are relevant for Math 422. Math 421 and 422 together will cover the all of the material from Math 321 but at a greater theoretical depth and a greater number of topics.
R statistical software:
You are advised to gain access to R statistical software. You have several options for this:
1) Install it on you computer
2) Use free online no-registration interfaces (this is a limited option)
3) Create a free account on RStudio Cloud (I highly recommend this option)
Here are instructions for getting R statistical software up and running on your computer (both for MAC and Windows). It should already be installed in all computer labs in Herak. If you find a computer where it is not installed, you can use these instructions to install it, or report it to me, and I will have IT install it.
Another option for having quick online access to R (and this is useful for a smartphone) is rdrr: https://rdrr.io/snippets/. This is just limited to computations not exceeding 10 seconds or so.
SageCell at: https://sagecell.sagemath.org/ is another useful option. This website can be used to evaluate commands from a variety of programming languages (including MATLAB and Python). Just select R from the language tab at the lower right of the textbox. If you are familiar with MATLAB, choose the option "Octave". Octave is essentially an open source version of MATLAB and you can run MATLAB code using the Octave language option on SageCell.
R miscellaneous:
Here is a website where you can evaluate R code online from your web browser from any device: https://rdrr.io/snippets/
Coin flipping simulation code.
Poker simulation code.
Here is a great R cheat sheet: https://rstudio.com/wp-content/uploads/2016/10/r-cheat-sheet-3.pdf
Course plan:
Here is a weekly outline of the course and material covered. This is a tentative plan, but we will likely not vary from this by more than a few days.
Tentative exam dates:
Studying and learning advice:
Studying is generally a very personal endeavor. You are advised to figure out what works for you. For most, mathematics is best learned by active engagement. Solving many problems and performing many calculations is advised. Often the best learning occurs when a problem is attempted multiple times with failure before succeeding.
Reflection is a key component to learning. Whether you solved a problem correctly or not or if you do or don't feel like you understand a particular concept, focusing on it with intent and active attention will help you make progress. Solving the same problem multiple times even if you already achieved the correct solution will help hard-wire the concepts and methodology in your brain. Try different approaches. Check for similar examples online or in other course materials. Mathematics Stack Exchange has a great wealth of information as well where many students have probably already asked the same questions you have. There are many other online math forums as well.
Persistence is absolutely necessary! You will be rewarded by your efforts!
A note about the quizzes, exams, and material coverage:
Quizzes generally only cover the material learned in the previous week or two. Each quiz is worth 25 points, and this can be thought of symbolizing that it is roughly one quarter of a regular exam in length. Normally quizzes are from 1-2 pages in length. They are timed for 15 to 25 minutes. The actual content may vary from 1-2 longer problems (i.e. longer more involved calculations) or 6-8 short problems (e.g. quick calculations, short answer, checking basic concepts, terminology, or multiple choice).
Regular exams only cover the new material since the last regular exam. Each regular exam is worth 100 points. Regular exams are normally 4-6 pages long and are timed for 50 minutes. You can use the quizzes as a rough guide for the exams, i.e. a regular exam will be roughly equivalent to four quizzes.
The Final Exam will cover any new material since the last regular exam and/or quiz and additionally will be comprehensive over the entire course. It is timed to 120 minutes, and thus can hypothetically be 2.4x the length of a regular exam. As a general guideline, you can expect it to be roughly equivalent to two complete exams.
These are only general guidelines and are meant to help you prepare for the quizzes and exams. Exams and quizzes are constructed so as to be able to be completed in the allotted time for a student who has sufficient preparation through attending class, studying, and completing all assignments with intention and effort.
You will want to check back here regularly as I may post a variety of course materials or links to various resources.
Syllabus
Video Lectures:
Chapter 14:
14.1-2 | video / R code text / pdf of notes
You should review some topics from chapters 3 and 4:
joint distributions, marginal and conditional distributions, and conditional expectations,
specifically sections 3.5,6,7 Multivariate, marginal and conditional distributions,
and 4.6 covariance, 4.8 conditional expectation
See my Math 421 review notes on that course page.
14.3 | Least squares regression - video / Rcode / dataset / jpg of notes
14.4-5 | Normal correlation and regression - video / Desmos plot / R code / jpg of notes / R code used to calc cond mean and var
Chapter 15:
One-way ANOVA | video / pdf of notes / R code / state covid data - metadata
Additional topic:
Rejection sampling | video / pdf of notes / R code
FREE Digital textbook access:
For free access to digital textbooks (good through May 25, 2020) sign up for a VitalSource account. You should be able to access most texts from most publishers. Here is more information: VitalSource Helps (go about 2/3 down to pink band on page). Sign up for a VitalSource Bookshelf account, and you can either download the local software or use a webrowser to view digital textbooks. There are also apps for various other devices. Bookshelf is their app for requesting access to and viewing digital testbooks.
I have successfully used VItalSource on both my laptop and phone.
Disclaimer: I haven't tested this free student access and do not know the exact procedure for gaining access to you textbooks digitally. It should NOT require any kind of payment information. Presumably, just create a Bookshelf account and there should be a way to search for your textbook and request access through that app.
Scanning work for turning in:
When turning in work via email, please convert it into a single high resolution pdf document (per assignment). This will make it easiest for me to keep everything organized and to write comments on the work to send back to you.
CamScanner is an app that I use to scan from phone to pdf. You can take multiple pictures and it will output a single pdf. It's available for both Android and iPhone. I am sure there are many similar apps. This one leaves a watermark with the free version. That's fine.
If you have a local scanner, that should work too. I prefer 300dpi and color, but 150dpi may suffice. Please check your pdf document so that the work is legible. Sometimes small writing or light writing (such as soft pencil) doesn't scan well. I suggest using blue or black ink or a sufficiently dark pencil for your written work. You could even try photos of boardwork, but make sure to organize it into a single document (per assignment).
Homework:
HW 1: Ch. 8 # 35,40,41,42,46,77,82
HW 2: Ch. 10 # 1,2,5,6,13,15,35,50,52,61,80
HW 3: Ch. 11 # 5 (just think about it and make an argument, no rigorous computations needed),
6 (the e is not the natural exponential e, maybe use a different letter if you like),
11 (hint: square and solve), 12, 19, 24, 36, 40, 53, 57
HW 4: Ch. 12 # 30,35,36,39,44
Ch. 13 # 19, 20, (25,26), (30,31,32), 44 (paired t-test), 49 (single variance),
63 (single proportion), 73 (multi-proportion), 76 (independence test),
81 (goodness of fit for Poisson)
HW 5: pdf - Due 4/15
GDP-CPI data
COVID-19 state data
video of my own exploration of the data using R
R code I used in the video
HW 6: pdf - Due Weds 5/6,
Use the state covid data linked above with the video.
See the metadata to understand what each column is.
Since the Date is in numerical format, you'll need to convert it to a factor with:
as.factor(d$Date) -> d$Date
Other Assignments:
Quiz 1: Due Wednesday 2/19. (Monday is a holiday)
Exam 1: Due Friday, 3/27. Turn in by sending a pdf via email.
Final Exam: Due Friday, 5/8. covid19 & population density dataset Submit via email as a single scanned pdf.
Review materials:
Here I will post additional review materials such as formula sheets or problems/solutions.
Course notes:
You are advised to acquire a copy of the textbook. I will provide some of my own notes as well in order to supplement the text.
See my Math 421 course page as well for some review materials.
You are free to look at my Summer 2019 Math 321 course page where I have the most recent complete version of my own probability/statistics notes. If I am teaching Math 321 in the current semester, you should check on that course's website for updated notes. These notes are not comprehensive over what Math 421/422 sequence covers, but you might find them helpful. Also, there are many review problems with solutions on that course page as well. Chapters 2,3, and 4 are most relevant for Math 421. Chapters 5,6,7 and 8 are relevant for Math 422. Math 421 and 422 together will cover the all of the material from Math 321 but at a greater theoretical depth and a greater number of topics.
R statistical software:
You are advised to gain access to R statistical software. You have several options for this:
1) Install it on you computer
2) Use free online no-registration interfaces (this is a limited option)
3) Create a free account on RStudio Cloud (I highly recommend this option)
Here are instructions for getting R statistical software up and running on your computer (both for MAC and Windows). It should already be installed in all computer labs in Herak. If you find a computer where it is not installed, you can use these instructions to install it, or report it to me, and I will have IT install it.
Another option for having quick online access to R (and this is useful for a smartphone) is rdrr: https://rdrr.io/snippets/. This is just limited to computations not exceeding 10 seconds or so.
SageCell at: https://sagecell.sagemath.org/ is another useful option. This website can be used to evaluate commands from a variety of programming languages (including MATLAB and Python). Just select R from the language tab at the lower right of the textbox. If you are familiar with MATLAB, choose the option "Octave". Octave is essentially an open source version of MATLAB and you can run MATLAB code using the Octave language option on SageCell.
R miscellaneous:
Here is a website where you can evaluate R code online from your web browser from any device: https://rdrr.io/snippets/
Coin flipping simulation code.
Poker simulation code.
Here is a great R cheat sheet: https://rstudio.com/wp-content/uploads/2016/10/r-cheat-sheet-3.pdf
Course plan:
Here is a weekly outline of the course and material covered. This is a tentative plan, but we will likely not vary from this by more than a few days.
| Week | Dates | Topic | Holidays | Chapters |
Tentative exam dates:
Studying and learning advice:
Studying is generally a very personal endeavor. You are advised to figure out what works for you. For most, mathematics is best learned by active engagement. Solving many problems and performing many calculations is advised. Often the best learning occurs when a problem is attempted multiple times with failure before succeeding.
Reflection is a key component to learning. Whether you solved a problem correctly or not or if you do or don't feel like you understand a particular concept, focusing on it with intent and active attention will help you make progress. Solving the same problem multiple times even if you already achieved the correct solution will help hard-wire the concepts and methodology in your brain. Try different approaches. Check for similar examples online or in other course materials. Mathematics Stack Exchange has a great wealth of information as well where many students have probably already asked the same questions you have. There are many other online math forums as well.
Persistence is absolutely necessary! You will be rewarded by your efforts!
A note about the quizzes, exams, and material coverage:
Quizzes generally only cover the material learned in the previous week or two. Each quiz is worth 25 points, and this can be thought of symbolizing that it is roughly one quarter of a regular exam in length. Normally quizzes are from 1-2 pages in length. They are timed for 15 to 25 minutes. The actual content may vary from 1-2 longer problems (i.e. longer more involved calculations) or 6-8 short problems (e.g. quick calculations, short answer, checking basic concepts, terminology, or multiple choice).
Regular exams only cover the new material since the last regular exam. Each regular exam is worth 100 points. Regular exams are normally 4-6 pages long and are timed for 50 minutes. You can use the quizzes as a rough guide for the exams, i.e. a regular exam will be roughly equivalent to four quizzes.
The Final Exam will cover any new material since the last regular exam and/or quiz and additionally will be comprehensive over the entire course. It is timed to 120 minutes, and thus can hypothetically be 2.4x the length of a regular exam. As a general guideline, you can expect it to be roughly equivalent to two complete exams.
These are only general guidelines and are meant to help you prepare for the quizzes and exams. Exams and quizzes are constructed so as to be able to be completed in the allotted time for a student who has sufficient preparation through attending class, studying, and completing all assignments with intention and effort.