Web page for Statistics 4 (which should be called Elementary Probability)

I am going to use these lecture notes, written by Stan Zachary. They have occasional references to

• D. Stirzaker (1999). Probability and Random Variables: a beginner's guide, Cambridge University Press.

• [GS] C.M. Grinstead and J.L. Snell (2006). Introduction to Probability, American Mathematical Society,

Other recommended books are:

• K.L. Chung and F. Aitsahlia (2003). Elementary Probability Theory, Springer-Verlag.
• G. Grimmett & D. Welsh (1990). Probability: an Introduction, Oxford University Press.
• S. M. Ross (1988). A First Course in Probability, 3rd edition, Macmillan.
• D. Williams (2001). Weighing the Odds: A Course in Probability and Statistics, Cambridge University Press.

[E1] This set of EXERCISES, is the primary source for problems which will be solved during the tutorial sessions. Exercises will be assigned weekly. You should try to solve them before coming to the tutorial session.
Answers to [E1].

[E2] These are ADDITIONAL EXERCISES (on background, supplements, etc.) In contrast to [E1], this file is DYNAMIC, i.e. its contents will be under continuous revision. So you will get no hard copy of it. But you are expected to be looking (and not only...) at it.

What you need to do for this module:

1. Attend lectures.
2. Study the lecture notes.
3. You are encouraged to study supplementary texts.
4. Solve the assigned exercises prior to the tutorial session.
5. Attempt to solve additional exercises from the recommended bibliography; for example, try the exercises from Grinstead and Snell and then look up the solutions in the file provided above.
6. At all times you need to be running a reality check regarding your background. If you have gaps, be brave and study some mathematics.
7. Ask questions.
8. Think, do not memorise.
9. You may find it helpful to study in groups, although taking exams in groups is strictly prohibited.
10. Go beyond classical studying and try to understand by experimenting, e.g. by following the links suggested below.

Assignments

1. From [E1]: Exercises 1-10.
   From [GS]: 2p35 (this means exercise 2 on page 35), 7p35, 11p36, 15p36, 26p39.
   Solutions to selected exercises
2. From [E1]: Exercises 11-18.
   From [E2]: Exercises 1-3.
   From [GS]: (15p15-optional), 17p15, 9p36, 15p36, 27p39.
   Solutions to selected exercises
   
3. From [E1]: Exercises 19-27.
   From [E2]: Exercises 4-7.
   Solutions to selected exercises (also check the email of 21/10/06 located in your mailbox or at the bottom of this page)
   
4. From [E1]: Exercises 28-33.
   From [E2]: Exercises 8-11.
   From [GS]: 3p197, 35p202, 1p219, 12p220.
   Solutions to selected exercises
   
5. From [E1]: Exercises 34-40.
   Solutions to selected exercises
6. From [E1]: Exercises 41-46.
   From [GS]: 22p282, 26p284, 27p284, 21p304.
   Solutions to selected exercises
7. From [E1]: Exercises 47-54.
   Solutions to selected exercises
   Solution to Ex.51 from [E1]

Test

Calculus Notes

Some facts from the lectures: click here

Midterm exam

Past exams

Links (more to come)

• Mathematica notebooks to accompany [GS]. You either need Mathematica 3.0 or the free Math Reader to view these notebooks.
• "Paradoxes" in probability: Six classical problems, with answers.
• This document explains how to compute probabilities in a Poker hand. It's a handout I gave to an elementary probability class I taught in the past.
• Nobody gave the correct definition of the derivative of a function. To remedy this (with a grain of salt), click here to find out how the derivative of a function is defined.
• Tha game of mines is an example of the use of the inclusion-exclusion formula.

Emails to the class

• Click here to see copies of emails sent to everyone. Note that the emails, as I promised to some students, contain additional points for thought.