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STAT401 Introduction to Probability (Fall 2016)
Instructor: Cheng Ouyang
Office Hours:
Monday, Friday: 4-5pm; Wednesday:3-4pm (or by appointment)
Location: SEO 502
Announcement:
Course Schedule:
| Weeks |
Sections |
Brief Description |
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08/22 - 08/26
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1.1; 1.2; 1.3.
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Introduction; Set Theory; Probability Set Function.
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08/29 - 09/02
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1.3; 1.4: 1.4.
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Probability Set Function; Conditional Probability and Independence.
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09/05 - 09/09
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Holiday; 1.5, 1.5
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Random Variables.
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09/12 - 09/16
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1.6; 1.7; 1.8
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Discrete Random Variables; Continuous Random Variables; Expectation
of a Random Variable.
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09/19 - 09/23
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1.9; 1.10; 2.1
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Special Expectations; Important Inequalities; Distributions of Two
Random Variables.
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09/26 - 09/30
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2.1; Review; Midterm I
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Distributions of Two Random Variables.
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10/03 - 10/07
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2.2; 2.2; 2.3
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Transformation: Bivariate Random Variables; Conditional Distributions and Expectations.
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10/10 - 10/14
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2.3; 2.4; 2.5
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Conditional Distributions and Expecation; Correlation Coefficient;
Independent Random Variables
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10/17 - 10/21
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2.6; 2.7; 2.7
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Extension to Several Random Variables; Transofrmations:
Random Vectors
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10/24 - 10/28
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2.8; 3.1; 3.2
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Linear Combination of Random Variables; Binomial and Related
Disbtributions; Poisson distribution
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10/31 - 11/04
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3.3; 3.4; 3.5
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Gamma, Chi-Squared and Deta Distributions; Normal Distribution;
Multivariate Normal Distribution
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11/07 - 11/11
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3.6; Review; Midterm II.
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t and F-Distributions
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11/14 - 11/18
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3.7; 5.1; 5.2
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Mixture Distributions; Convergence in Probability;
Convergence in Distribution |
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11/21 - 11/25
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5.2; 5.3; Holiday
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Convergence in Districution; Central Limit Theorem
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11/28 - 12/02
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5.3; 5.3; Review
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Central Limit Theorem
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(We are currently two lectures behind the planned course schedule.)
Homework (updated weekly):
- §1.2: 1, 11, 12, 15; §1.3: 1, 2, 4, 5. (due on
08/31) (solution)
- §1.4: 3, 5, 7, 8, 34. (due one 09/07) (solution)
- §1.5: 2, 5, 6, 7; §1.6: 2, 8, 9. (due on 09/14) (Due date is extended to Friday, Sep 16) (solution)
- §1.7: 1, 3, 6, 14, 21; §1.8: 2, 3, 6, 9. (due on 09/21) (solution)
- §1.9: 1, 2, 18; §1.10: 2, 3. (due on 09/28) (solution)
- §2.1: 1, 10, 12, 13, 16. (due on 10/05) (solution)
- §2.2: 1, 2, 3, 5(a); §2.3: 1, 2. (due on 10/12) (Due date is extended to Friday, Oct 14) (solution)
- §2.3: 4, 7, 8; §2.4: 1, 3, 10. (due on 10/19) (solution)
- §2.5: 1, 2, 3, 8, 9; §2.6: 1(a), (c), (d), (f), (g),
3. (due on 10/26) (solution)
- §2.7: 1, 4; §2.8: 2, 5, 6; §3.1: 4, 5, 6. (due on
11/2) (solution)
- §3.2: 1, 8, 10; §3.3: 2 (Hint:
chi^2(r)=gamma(r/2,2)) (due on 11/09) (solution)
- §3.4: 2, 3, 4. (Note: In the book, the 2nd parameter for
N(mu, sigma^2) is variance instead of standard deviation.);
§3.5: 1. (due on 11/23) (solution)
- §5.1: 2, 3, 5; §5.2: 1, 2. (due on 12/02) (solution)
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