Stat 61 - Probability and Mathematical Statistics I

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This is the home page for Statistics 61.

12/13/07 - And here's a solution sheet for hw 9. One set of solutions is missing, but this is what there is.

61solutions9.doc - Word document

12/3/07 - Here's homework 9:

61homework9.doc - one page Word document; homework due 12/10.

There are routine problems on hypothesis tests and "t" distributions, and a challenge to do a regression in Excel (or any other software). We'll talk about Excel for regressions on Wednesday.

11/28/07 - Here are the two PowerPoint presentations from class today. As you can tell from the filenames, they are both from a Stat 11 class a couple of years ago. The second one has extra material at the end about the "regression effect."

Stat11-30Jan06.ppt

Stat11-1Feb06.ppt

11/26/07 - At last, here is homework 8 on line:

61homework8.doc - one page Word; due 11/26.

11/13/07 - Here is Solutions #7.

11/7/07 - Two links:

61solutions6.doc - solutions 6 (5-page Word, 11/7/07)

61notes7nov07.doc - handout in class 11/7, on Jensen's inequality and applications to HM < GM < AM < RMS

11/5/07 - Homework #6 is due Wednesday, not today. But, here's homework 7 already:

61homework7.doc - homework 7 (3-page Word, 10/5/07, due 11/12/07)

61homework7.htm - homework 7 (web version)

Also, here is the three-page handout from class:

61notes5nov07.doc

(I might enter my own solutions soon, so watch this space.)

10/30/07 - Solutions #5 are posted under "course documents."

10/28/07 - Handout on descriptive statistics for class 10/29:

descriptive-2007.doc (Word with MathType and graphics, 5 pages)

Also, homework 6 (problems may be added, depending on how far we get Monday):

61homework6.doc - Word version

61homework6.htm - html version

10/22/07 - Homework 5 is now posted under "course documents," below. There is a reference to the "secret formula," which is:

E(X) = integral for x=0 to infinity of (1-F(x))dx minus integral for x=-infinity to 0 of (F(x))dx

(provided both integrals exist and are finite)

10/10/07 - Here are the instructions for the exam (the ones that are still inside the envelope):

You may take up to three hours for this exam, at a time and place of your choosing. You may use a calculator. You may not consult any reference or any person other than the instructor. You may answer on the test itself or on your own paper, or any combination. You do not need to turn in scratch paper. Return the exam in class, to my office, or to the math department office by 11:30am Friday, October 12.

10/8/07 - The solution set for homework 4 is under "course documents."

10/7/07 - Two new items:

(1) What's on the exam?

(2) CountableSets1.doc (4-page Word with graphics) -- A
short essay on "countable" and "uncountable" sets. We didn't really say
much in class about what these are, and it matters. So, if you aren't already
comfortable with the distinction between countable and uncountable sets, try the essay.

10/1/07 - Jump to "course documents" (below) for HOMEWORK 4 and SOLUTIONS 3. Note that the paper version of homework 4 has an error in problem 3c; there should be a factor of "k-squared" before the first left parenthesis.

9/29/07 - Here's homework 3, due 10/1/07:

web version: 61homework3.htm

WORD version: 61homework3.doc

9/28/07 - Solution set for homework 2: 61solutions2.doc
(Word with MathType) (* corrected 9/29/07 *)

There is definitely no exam on September 28.

9/21/07 - Solution set for homework 1: 61solutions1.doc (5-page Word with MathType)

9/20/07 - Two corrections to homework 2:

(1) In problem 4b, the "hard way" should be:

P(K) = P(first card is king) P(K|first card is king) + P(first card NOT king) P(K|first card NOT king)

(2) In problem 7: the reference to A1, A2, A3 should of course be to A4, A6, A8.

The corrections are made on the web version of the homework (link below). A possible third correction: 8b and 8c are silly questions; they don't work the way I thought they did. But, I have left them in the homework.

9/19/07 - Richardson and Stone on the Scorpion search: ScorpionSearch.pdf

9/19/07 - Newton and Pepys: PepysAndNewton.pdf

Homework 2, due 9/24/07:

web version: 61homework2.htm

WORD version: 61homework2.doc (two pages)

I'm looking for careful proofs from the axioms and definitions on problems 1 and 2. That means that you can freely use any true statement about arithmetic or logic, but any statement about events and their probabilities should be based on the assumptions and definitions in class or in the book. For the other problems---be precise as usual, but you don't need to work from the axioms.

While we're filling in links... Here's that PowerPoint presentation about the Scorpion search, originally from Bryn Mawr in 2005:

SearchTalk.ppt

Also, here's a link to the newest Scorpion book at Amazon. (If it doesn't work search on Amazon for "Offley Scorpion Down".) The customer reviews include some opionions about whether Offley's conclusions are sound.

9/8/07 - Here's an advance version of Homework 1, due 9/17/07:

web version: 61homework1.htm

WORD version: 61homework1.doc

9/3/07 - Here is the spreadsheet left over from class today:

waitingtimes-03sep07.xls

(Excel tricks: Selecting a block of cells and naming it by typing the the "name" box and pressing "Enter", INT(), RAND() functions, and COUNTIF function with constructed second argument.)

We decided that the formula for the probability distribution function is

F(a) = [probability that a waiting time is <=a] = 1-(1-p)^a

where p is (at least roughly) the probability of a taxi-event in any one second interval. This translates to

F(a) = 1-exp(-a/m)

where m is...well, what, exactly?

8/16/07 - We have a text:

Larsen and Marx, *An Introduction to Mathematical Statistics and
its Applications,* 4rd ed., Prentice Hall, ISBN 0-13-186793-8.

This is a newer edition of the text that has been used for the last several years. If you already own the third edition, it might suffice --- I won't take offense, but the risk is yours. The fourth edition includes a significant reorganization of the probability chapters.

descriptive-2007.doc - notes on descriptive statistics, for class 10/29/07 (5-page Word with MathType and graphics)

61homework7.doc - homework 7 (3-page Word, 10/5/07, due 11/12/07)

61homework7.htm - homework 7 (web version)

61solutions7.doc - solutions 7 (Word, 11/12/07)

61homework6.doc - homework 6 (2-page Word, 10/29/07, due 11/5/07) (due date changed to 11/7)

61homework6.htm - homework 6 (web version)

61solutions6.doc - solutions 6 (5-page Word, 11/7/07)

61homework5b.doc -- homework 5 (3-page Word, 10/22/07, due 10/29/07)

61homework5b.htm -- homework 5 (web version)

61homework5a.doc -- draft of homework 5 (2-page word, 10/12/07) - superseded by above

61solutions5.doc -- solutions to homework 5 (Word with MathType, 10/29/07)

61homework4.doc -- homework 4 (3-page Word, 10/1/07, due 10/8/07)

61homework4.htm -- homework 4 (web version)

61solutions4.doc -- solutions to homework 4 (7-page Word with MathType, 10/8/07)

61homework3.doc -- homework 3 (1-page Word, 9/26/07, due 10/1/07)

61homework3.htm -- homework 3 (web version)

61solutions3.doc -- solutions to homework 3 (10/1/07, Word)

61homework2.doc -- homework 2 (2-page Word, 9/19/07, corrected 9/20/07, due 9/26/07)

61homework2.htm -- homework 2 (web version)

61solutions2.doc -- solutions to homework 2 (5-page Word, 9/24/07, corrected 9/29/07)

61homework1.doc -- homework 1 (2-page Word, 9/8/07, due 9/17/07)

61homework1.htm -- homework 1 (web version)

61solutions1.doc -- solutions to homework 1 (5-page Word, 9/21/07)

61Schedule.htm -- schedule (as of 9/30/07)

61Schedule.xls -- schedule (as of 9/30/07) (Excel version)

61Schedule0.xls -- schedule (original, as of 8/16/07) (Excel version)

61CourseInfo.html -- syllabus (preliminary 8/16/07)

**Course info: (or see **syllabus**)**

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**Class:** Science Center L26, MWF 11:30-12:20am.

**Instructor:**
**Walter Stromquist**

Office: Science Center 159.

Office hours: tbd

Email: wstromq1@swarthmore.edu

Phone: Cell 610-220-4382 (ok to leave messages).

Office phone 610-690-6827 (please don't leave messages).

For snow emergencies on class days, call the office phone 610-690-6827 after 9:30am.

**Text:** Larsen and Marx, *An Introduction to Mathematical Statistics and
its Applications,* 4rd ed., Prentice Hall, ISBN 0-13-186793-8.

**Coverage:** We'll cover probability (chapters 2-4) during the first six or seven weeks, and then study estimation of parameters (chapters 5 and 7), hypothesis testing (chapters 6 and 7), and linear regression (chapter 11).

**Web site:**
http://www.swarthmore.edu/NatSci/wstromq1/stat61/index.html

**Course requirements:**

Homework (about 15% of grade) - due weekly on Mondays.
Collaboration is encouraged but you must prepare your own answers.

Four interim exams (15% each) - Tentatively due Sept. 28, Oct. 26, Nov. 16, Dec. 7. Some will be self-scheduled or take-home.

Final exam (25%)

**From the catalog:** "This course introduces the mathematical
theory of probability, including density functions and distribution
functions, joint and marginal distributions, conditional probability,
and expected value and variance. It then develops the theory of
statistics, including parameter estimation and hypothesis testing.
The emphasis is on proving results in mathematical statistics rather
than on applying statistical methods. Students needing to learn
applied statistics and data analysis should consider STAT 011
or 031 in addition or instead of this course."

Before 2006 this course was called STAT 53. It is the prerequisite for both the probability seminar (MATH 105) and the statistics seminar (STAT 111). The prerequisite for STAT 61 is some form of several-variable calculus (MATH 23, 33, or 34) or the consent of the instructor. Linear algebra is not a prerequisite.

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