Math 2030 M Course Information

• Poisson distribution: 2.4: 4 and 3.5: 2, 8, 10ab, 11a
• Geometric distribution: 3.4: 4
• Exponential distribution: 4.2: 3bc, 4abc

Assignment 7 due noon on Monday, March 26. Section 3.2: 14, Section 4.1: 2bc, 3e, 9, Section 3.3: 2, 3, 8bc, 12, 14, 20.

For all x, F(x) = F(x+) = lim _{y-->x, y > x} F(y) .

I will be on campus in the afternoon on Friday.

Please pass this information around as not everyone checks this page.

Consider a hat with 10 cards of which 3 are white on both sides, 5 black on one side and white on the other, 2 black on both sides. A card is drawn from the hat. As a black side is visible, the card must be one of the 7 cards with black sides. Of them, 5 have white as the other side, so the answer to the question 8. is 5/7.

To submit, use the assignment box for the course which is across from the North 5th floor Ross elevators. Late homework will not be accepted.

Assignment 1: Carefully present solutions to the following questions:

• Section 1.1: 2, 7, 8
• Section 1.3: 4, 6, 9, 10
• Appendix I: viii, x, xiii.

Lecturer: Eli Brettler
Office: South 508 Ross
Telephone: 736-2100 Extension 66321
E-mail: brettler@mathstat.yorku.ca
WWW: http://www.math.yorku.ca/Who/Faculty/Brettler/
Normal Office hours: By appointment. I am normally available Tuesday and Wednesday afternoon.

Lectures: MWF 8:30 - 9:30 VH C.
There are no lectures or tutorials February 20 - 24 (Winter Reading Week).

Tutorials: Tutorial assistance is available M - F from 10:30 - 3:30 in the MathLab, South 525 Ross.

Text: Probability by Jim Pitman.

Expected textbook coverage: Chapter 1 (except Empirical distributions in 1.3), Chapter 2 (except skew normal approximations in 2.2, odds ratios in 2.3), Chapter 3 (except negative binomial distribution in 3.4, skew normal approximations in 3.5), Chapter 4 (except gamma distribution in 4.2, hazard rates in 4.3, order statistics in 4.6), Chapter 6 (Section 6.4), Appendix 1.

Evaluation:

Homework	Various	15%
Class Tests	February 6, March 16	40%
Final Examination (three hours)	April Examination Period (April 4 - 20)	45%

Submit homework on time. Late homework will not be accepted for grading.

There will be no makeups for missed class tests. If you miss a test for medical (or other unexpected and unavoidable) reasons and provide appropriate (medical or other) documentation, its weight will be transferred to the final examination and a grade will be assigned based on your relative performance on the exam. Otherwise, the mark for the missed work will be 0.

Do not make April travel arrangements prior to the announcement of the April examination date.

Note: Students must bring appropriate photo identification to all tests and exams.

Lecture Resource: Professor Salisbury has provided the following detailed outline. His slides from Winter 2011 are available by clicking on the links below.

• Part I:
  • The model for probabilities, random variables, and events (Sections 1.1 - 1.3) [omit: empirical distributions]
  • Counting (appendix 1)
• Part II
  • Independence and Conditional Probability (Sections 1.4 and 1.6)
  • Bayes rule (Section 1.5)
• Part III (corrected)
  • Representing discrete and continuous distributions (Sections 3.1 [pp. 140-141] and 4.1 [pp. 259-271])
  • Cumulative Distribution functions, their relation with densities and discrete distributions (Section 4.5)
  • Using cdf's to compute distributions of transformed random variables (Section 4.5, pp. 320-323)
• Part IV (corrected)
  • Binomial and Normal distributions (Sections 2.1 and 2.2),
  • Normal approximations to the binomial distribution (Section 2.2) [omit: skew normal approximation]
  • Expectations for discrete and continuous random variables (Section 3.2, and pp. 273-275 of Section 4.1), including the method of indicators.
  • Variances (pp. 185-189 of Section 3.3), along with calculation of means and variances for distributions like the Binomial and Normal.
  • The hypergeometric distribution (Sections 2.5 and 3.6)
• Part V (version v)
  • Independence of random variables (p. 151 of Section 3.1), and its consequences for expectations and variances (p. 193 of Section 3.3).
  • The law of large numbers, Chebyshev's inequality, and the Central Limit Theorem (pp. 191-197 of Section 3.3)
  • Normal approximations to more general sums of independent random variables (p. 196 of Section 3.3).
  • The Poisson distribution and Poisson approximation (Sections 2.4 and 3.5)
  • The geometric distribution (Section 3.4)
  • The exponential distribution and relation to the Poisson (Section 4.2)
  • The negative binomial and gamma distributions (Sections 3.4 and 4.2: were mentioned, but you're not responsible for them.)
  • Joint and marginal distributions, correlation and covariance (for discrete r.v. only) (Sections 3.1 and 6.4)

Test and Homework Solutions:

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Note: The last date to drop the course without academic penalty is March 9. It is extremely important that you realistically assess your course performance prior to this date.