Elementary Probability

**Lectures:** 7:00 - 10:00 Stedman Lecture Hall B

**Office hours:** (tentative) Monday 2:00-3:00,
Wednesday 2:30-4:00, Friday 1:00-2:00; or by appointment

**Tutorials:** The dedicated problem sessions for this
course are scheduled for Wednesday at 3:30, and Friday at 12:30,
both in N501 Ross Building. (Begins January 15.)

**Text:** *Probability*, by Jim Pitman
(Springer-Verlag, 1993).

**Prerequisite:** A course in multivariate calculus
(see calendar for details).

**Syllabus:**

Number of hours Section Topic (approx.) 1.1-1.6 Introduction 6 2.1-2.2, 2.4-2.5 Repeated trials and sampling 6 3.1-3.5 Random variables 7 4.1-4.2, 4.4-4.5 Continuous distributions 7 5.1-5.2 Continuous joint distributions 5 6.1, 6.3 Conditional probability: discrete case 5

Homework 10% Two term tests (25% each) 50% Final Examination 40%

The second test will be March 27, from 7:00-8:00. It will cover Sections 2.2, 2.4, 3.3, 3.4, 3.5, 4.1, 4.2, 4.4, 4.5 (excluding skewness and Poisson scatter). You may bring a calculator, but no other aids are permitted.

The Final Examination will be scheduled during the Spring Examination Period and will be a common exam with the other section of the course.

**Additional Important Information:**

1. Each student should do at least two hours of independent study for
every lecture hour. It is recommended that each student read
the relevant sections of the text before each lecture.

2. Homework will be assigned most weeks, due the following week (unless
there is test that week). Solutions will be avaliable on the evening that
the homework is due, and therefore late assignments will NOT be
accepted.

3. This course will follow the schedule of the Faculty of Arts, not
Atkinson College. That is: there will be a class every Wednesday up
to and including April 10, except for February 27 (reading week).
(Note: There will be a class on April 3, the first night of Passover.)
See the detailed schedule below.
The final exam will be a three-hour exam during the April 15-30 exam period.

4. The last date to withdraw from this course without academic penalty is March 9.

**Homework Problems**

Note: EXPLAIN your answers. (This is especially important when
the numerical answers are provided in the back of the book!)

Sections 1.1-1.3:

(a) To be handed in on January 17: Exercises
1.1.4, 1.1.8(a-d; in part d, replace
"6" by "n"), 1.3.2, 1.3.6, 1.3.10(a), 1.3.13.

(b) Other problems to work on (especially those marked *)
(not to be handed in):
1.1.3, 1.1.5*, 1.1.7, 1.1.9, 1.2.3, 1.3.5, 1.3.9, 1.3.11.

Sections 1.4-1.6:

(a) To be handed in on January 24:
Exercises 1.4.4, 1.4.5, 1.5.2, 1.5.5, 1.6.4, 1.6.6.

(b) Additional problems (not to be handed in):
1.4.3, 1.4.7, 1.4.9; 1.5.1, 1.5.4;
1.6.3, 1.6.7; Review (pages 74-77): 5, 7, 11, 13, 15, 17.

Sections 2.1 and 2.5:

(a) To be handed in on Wednesday, January 31:
Exercises 2.1.3, 2.1.4, 2.1.6; 2.5.7, 2.5.9,
2.5.12(c,d,f). (NOTE: In 2.5.12, the letters a,b,c stand for
different ranks.)

(b) Additional problems (not to be handed in):
2.1.1, 2.1.11, 2.1.13, 2.1.15(a,b); 2.5.1, 2.5.3, 2.5.10.
Review (pages 132-137): 1, 3, 5, 17, 25(b,e), 33.

Sections 3.1 and 3.2:

(a) To be handed in on Wednesday, February 7:
Exercises 3.1.2, 3.1.6, 3.1.16; 3.1.18(a); 3.2.5, 3.2.9, 3.2.13.

(b) Additional problems (not to be handed in):
3.1.3, 3.1.7, 3.1.11, 3.1.12, 3.1.19, 3.1.24(a), 3.2.3, 3.2.11,
3.2.19.

Sections 3.3 and 2.2:

(a) To be handed in on Wednesday, February 21:
Exercises 3.3.3, 3.3.6, 3.3.12, 3.3.20; 2.2.9, 2.2.12.

(b) Additional problems (not to be handed in):
3.3.5, 3.3.7, 3.3.9, 3.3.13, 3.3.19, 3.3.23; 2.2.1, 2.2.3.

Sections 2.4 and 3.4:

(a) To be handed in on Wednesday, March 6:
Exercises 2.4.4, 2.4.6(b), 3.4.4, 3.4.8, 3.4.12(a,b,d).

(b) Additional problems (not to be handed in):
2.4.5, 2.4.9, 3.4.1, 3.4.5, 3.4.11, 3.4.19.

Sections 3.5 and 4.1:

(a) To be handed in on Wednesday, March 13:
Exercises 3.5.5, 3.5.9(c), 3.5.10(c), 3.5.12, 4.1.4, 4.1.6(a), 4.1.12(a).

(b) Additional problems (not to be handed in):
3.5.3, 3.5.9(a,b), 3.5.11, 3.5.13, 4.1.3, 4.1.9.

Sections 4.2 and 4.4:

(a) To be handed in on Wednesday, March 20:
Exercises 4.2.4, 4.2.8(a,b), 4.2.12(a,b), 4.4.6, 4.4.10(b).

(b) Additional problems (not to be handed in):
4.2.5, 4.2.7, 4.2.9*, 4.4.3, 4.4.9.

Sections 5.1 and 5.2:

(a) To be handed in on Wednesday, April 3:
Exercises 5.1.2, 5.1.4(a), 5.2.4, 5.2.8(a,c), 5.2.12.

Sections 6.1 and 6.3:

(a) To be handed in on Wednesday, April 10:
Exercises 6.1.2, 6.1.3, 6.1.4, 6.3.2(a,b), 6.3.11.

(b) Additional problems (not to be handed in):
6.1.1, 6.1.7, 6.3.1, 6.3.5(a,b).

** Plan of lectures for the term** (by section of the text):

January 10: 1.1, 1.2, 1.3

January 17: 1.4, 1.5, 1.6

January 24: 2.1, 2.5

January 31: most of 3.1 and 3.2

February 7: 3.3 (and rest of 3.1/3.2)

February 14: Test #1, and 2.2

February 21: 2.4, 3.4

February 28: No class (reading week)

March 6: 3.5, 4.1

March 13: 4.2, 4.4

March 20: 4.5, 5.1

March 27: Test #2, and 5.2

April 3: 6.1, 6.3

April 10: 6.2, 6.4

Last modified: April 2, 1996