Solutions to homework 10 are posted here.
Solutions to homework 9 are posted here.
Solutions to homework 8 are posted here.
Solutions to homework 7 are posted here.
A brief proof that the correlation of two random variables is bounded between -1 and 1 is available here.
A set of notes from when I took a similar course to STAT400 as an undergrad are available here. Keep in mind that these are only a skeleton of what you should know. But like a skeleton, without knowing this material, you have little chance of standing. Also, I again point you to the Probability and Statistics Cookbook. It really is a fantastic compressed source of some of the material you should know.
Solutions to homework 6 are posted here.
Partial Solutions to homework 5 are posted here. Please note the following errors: in 20b, in finding the second interval for the percentile function, I should have moved everything to the right hand side before applying the quadratic formula to solve for y as a function of p. If this procedure is not clear, please do not hesitate to ask. Also, in 30c, I misread the standard normal table. The percentile value should be ~0.675, not ~0.775.
Solutions to homework 4 are posted here. Please note the following errors: in 32a, I failed to compute the square of the expectation when using the computational definition of variance. Thus, this answer is wrong, as well as 32c, which uses this value. Also, in 48b, I read the incorrect value off of the binomial table, so this probability is wrong.
A brief exposition on why Bayes’s rule is important can be found here.
(Partial) Solutions to homework 3 are posted here. Please note: I misread the information in Problem 2.4.66, and as such my solution is not correct based on the information given. In fact, as I misread it, we would not be able to compute part C.
Solutions to homework 2 are posted here.
Solutions to homework 1 are posted here.
The first meeting for our discussion section will be Monday, September 12. Please come prepared with questions on the material you have covered in your homework and during lecture.
Office Hours: Wednesday, 10am - 12pm in CSS 4364
Some External Resources
Can one learn mathematics by reading it? I am inclined to say no. Reading has an edge over listening because reading is more active -- but not much. Reading with pencil and paper on the side is very much better -- it is a big step in the right direction. The very best way to read a book, however, with, to be sure, pencil and paper on the side, is to keep the pencil busy on the paper and throw the book away.
- Halmos, from The Problem of Learning to Teach
This is a 400 level statistics course. As such, a great deal of learning should and must occur outside of the lecture hall and recitation room. That means a great deal of learning will happen on your time, whether its crammed right before the exams or spread out leisurely over the course of the semester. A good deal of that time should be spent with the textbook. You’ve spent upwards of $100 on the thing. To put that into perspective, that’s ten trips to the movie theater, one day at Disney world, or 120 cans of Bud Light. You might as well get the most out of it! See the following article for a gentle introduction to reading mathematical works:
- How to Read Mathematics by Shai Simonson and Fernando Gouvea
Another skill that you will learn (eventually) as scientists and engineers is to look to many different sources of information on a given topic. It is possible, in fact probable, that you will understand a presentation of the material covered in the class better from someone who is not myself, the lecturer, or the textbook. For some places to start, check the videos and problems at the Khan Academy and the course notes at MIT OpenCourseware:
It is often useful to write up your notes after a lecture. Fortunately, with the ubiquity of mathematical material on the web, you can often find ready-made summaries. The following link points you to a probability and statistics ‘cookbook.’ Mathematics is about much more than memorization, but it’s rather hard to prove a theorem if you don’t remember the definitions involved. This cookbook also contains far more material than will be covered in this course. Consider it a sneak peak if you plan to become a probabilist or statistician (or even a well-informed scientist).