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STA 257  Probability and Statistics
I  Fall 2002
Unofficial final marks for the course are here.
They are sorted by the last 5 digits in
your student number.
Term Test:
There will not be any adjustment to the grades.
Summary statistics for grades:
Mean: 46.8/70=67%
Median: 49/70=70%
Standard deviation: 13/70=18.6%
Maximum: 70/70=100%
Term test solutions in pdf
Marks for the term test and first 9 quizzes are here.
They are sorted by the last 5 digits in
your student number.
Students whose mark is a dot did not write the test/quiz.
A mark of 999 indicates that valid documentation was received for a missed
test. Two tutors had not yet recorded the grades for quiz 9 for their
tutorials. For these students, their quiz 9 grade is currently recorded
as 111.
Course outline in pdf
Lecture notes:
A copy of the overhead transparencies from Lecture 2 on is available in
shortterm loan at the
Gerstein Library effective Friday, September 19.
Ask for the lecture notes for STA257. A copy of the textbook can also be
borrowed for 2 hours from the shortterm loan desk. Ask for call number
178 for the text and 179 for the student solutions manual.
Where else you can get help with the course material (until Friday, December 6):

Statistics Aid Centre SS 2133
Wednesdays 11:001:00 (last day: December 4)
Staffed by one of the course teaching assistants.

New College 55B (until Friday, December 6)
Mondays 9:001:00
Wednesdays 9:0012:00 and 1:004:00
Thursdays 9:0012:00
Fridays 9:0012:00
Staffed by graduate students in Statistics.
Additional office hours before the exam:
Monday, December 9:
10:0012:00 A. Gibbs SS 6026E
1:004:00 Mohammed S. SS 2101
Tuesday, December 10:
10:0012:00 A. Gibbs SS 6026E
12:002:00 Shuying SS 2120
2:005:00 Xiaobin SS 2120
Wednesday, December 11:
2:004:00 Yan SS 2120
Hanna and/or John will be in New College 55B on Monday, December 9
from 9:00 to 1:00 and Wednesday, December 11 from 9:00 to 4:00
Practice problems:

Practice Problems 1
For quiz in tutorial on Wednesday, September 18
Solutions to additional questions from Practice Problems 1

Practice Problems 2
For quiz in tutorial on Wednesday, September 25
For quiz on September 25 you can omit questions 10, 13, and 14 from
Practice Problems 2. The required material for these questions will be
covered in lecture on Monday, September 23. These problems should be completed
for Wednesday, October 2.
Solutions to additional questions from Practice Problems 2

Practice Problems 3
For quiz in tutorial on Wednesday, October 2
To do the variance calculation in questions 4.35 from the text and
12 from the additional questions, you will need the properties of variance
that we will cover at the beginning of Monday's lecture.
Solutions to additional questions from Practice Problems 3

Practice Problems 4
For quiz in tutorial on Wednesday, October 9
To do questions 2.39, 2.45(c) and additional questions 10, 11, and 12
you will need material that will be covered
in lecture on Monday, October 7. (So they won't be covered on the quiz on
October 9.)
Solutions to additional questions from Practice Problems 4

Practice Problems 5
For quiz in tutorial on Wednesday, October 23 (no quiz on October 16)
To do questions 5.7(c), 5.8(c), 5.51(c) and 5.67 and additional questions
5(e) and 7(e)
you will need material that will be covered
in lecture on Monday, October 21. (So they won't be covered on the quiz on
October 23 but will be covered on the midterm test. Note that for most of
these questions you should do all parts expect the part mentioned
above.)
Solutions to additional questions from Practice Problems 5
Correction to solutions to practice problems 5:
Answer to 5.8(c) from Schaeffer should be 1/3. The upper limit of the
integral should be 3/4. Also the exponent on the lambda in the answer
for 9(e) should be 3 (not 2). (Correction posted October 25, 3:00 p.m.)

Practice Problems 6
For quiz in tutorial on Wednesday, November 6
#12 has been moved to Practice Problems 7
Solutions to additional questions from Practice Problems 6

Practice Problems 7
For quiz in tutorial on Wednesday, November 13
Correction answer to #4: EY=mu/lambda.
Solutions to additional questions from Practice Problems 7

Practice Problems 8
For quiz in tutorial on Wednesday, November 20
Exercise 7 should read that the means are 1/lambda and 1/mu.
Exercise 4.73 from the textbook has been moved to Practice Problems 9.
Solutions to additional questions from Practice Problems 8

Practice Problems 9
For quiz in tutorial on Wednesday, November 27
Corrections to answers on Practice Problems 9:
#4: m and n are reversed in answer; X and Y should be assumed independent.
#6: exponent on y should be beta1.
You are not responsible for exercise 6.29 from the text.
Solutions to additional questions from Practice Problems 9

Practice Problems 10
For quiz in tutorial on Wednesday, December 4
Exercise 7.9 uses the fact that often a good estimate of the standard
deviation is the range/4. We didn't discuss this, and you're not responsible
for this estimate of standard deviation on the exam.
Solutions to additional questions from Practice Problems 10
The derivatives in the solutions to 7(a) are incorrect.
Statistics handout for material covered in last week of classes
Solutions to problems on statistics handout
Corrections to solutions of statistics handout:
#5: g'(s)=2(n1)s/sigma^2, i.e. the s should not be squared in
the derivative. The
rest of the solution is correct.
#6(b): Should get 4p(1p)>n/(1+2n) (the "2" is missing in the original
solution). Note that n/(1+2n) is now not equal to 1 for large n, however
the diagram is still correct, and the parabola is still above the xaxis
for p near 1/2, so the answer is still the same.
Practice term tests:
The following two term tests (in pdf) were given in 1996 when I last taught this
course. They give an indication of the level of difficulty that can
be expected on the test on October 28.
Term Test 1 from Summer, 1996
Solutions to Term Test 1 from Summer, 1996
Term Test 2 from Summer, 1996
Solutions to Term Test 2 from Summer, 1996
Corrections to solutions: #4 The second covariance on the 4th line should
be Cov(X_1,X_3) NOT Cov(X_2,X_3).
The term test on October 28, 2002 will include the material covered
on test 1 from 1996 and the first 3 questions on test 2 from 1996.
Practice final exam:
The following exam was given in 1996 when I last taught this course.
Final exam from Summer, 1996
Solutions to final exam from Summer, 1996
#14 uses Markov's inequality (not Chebyshev's).
Formulae that will be provided on final exam (December, 2002)
Note that a geometric random variable can be defined in two ways:
as the number of failures before the first success, or as the trial number
on which the first success occurs. The probability function on the formula
sheet is for the first way, your textbook uses the second way. Any questions
on the exam using the geometric distribution are very clear about what
the random variable is measuring in relation to the probability function.
Email course instructor: alison.gibbs@utstat.utoronto.ca