STAT 501 - Cheng Ouyang
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STAT501 Probability Theorey (I) (Fall 2019)

Instructor: Cheng Ouyang

Office Hours:

Time: Monday and Friday 4-5pm (or by appointment)
Location: SEO 502

Syllabus

Announcement:

Course Schedule (updated weekly):

Weeks Sections Brief Description
08/26 - 08/30 1.1; 1.2; 1.3 Introduction; Basic Set Theory; Limits of Sets
09/02 - 09/06 Holiday(Monday); 1.4; 1.5 Limits of Sets and Monotone Sequences; Set Operations and Closure.
09/09 - 09/13 1.6 and 1.7; 1.8; 2.1 The sigma-field Generated by a Given Class; Comparing Borel Sets; Basic Definition and Properties of Probability Spaces
09/16 - 09/20 2.1; 2.2; 2.2 Basic Definition and Properties of Probability Spaces; More on Closure
09/23 - 09/27 2.3 and 2.4; 2.4; 2.4 Two Constructions; Constructions of Probability Spaces
09/30 - 10/04 2.4; 2.4, 2.5; 2.5 Constructions of Probability Spaces; Measure Constructions
10/07 - 10/11 3.1; 3.2; 3.2. Inverse Maps; Measurable Maps, Random Elements, Induced Probability Measures.
10/14 - 10/18 3.3; 4.1, 4.2; 4.2. Sigma-Fields Generated by Maps; Basic Definitions of Independence, Independent Random Variables.
10/21 - 10/25 4.4; 4.5; 4.5; More on Independence: Groupings; Independence, Zero-One Laws, Borel-Cantelli Lemma.
10/28 - 11/01 4.5; 5.1, 5.2; 5.2 Independence, Zero-One laws, Borel-Cantelli Lemma; Preparation for Integration; Expectation and Integration
11/04 - 11/08 5.2; 5.3; 5.4. Expectation and Integration; Limits and Integrals; Indefinite Integrals;
11/11 - 11/15 5.4; 5.5; 5.6, Indefinite Integrals; Transformation Theorem and Densities; Riemann vs Lebesgue Integral.
11/18 - 11/22 5.7, 5.8; 5.9; 5.9. Product Spaces, Probability Measures on Product Spaces; Fubini's Theorem.
11/25 - 11/29 5.9,6.1; Holidy (Friday) Fubini's Theorem, Almost Sure Convergence; Convergence in Probability; Connections between a.s. and i.p. Convergence.
12/02 - 12/06 6.2; 6.3; 6.5 Convergence in probability; Connections between a.s. and i.p. convergence; Lp Convergence

Homework (updated weekly):

  • Homework #1 (due on 09/04): 1.9 - 6, 19.
  • Homework #2 (due on 09/11): 1.9 - 10, 14, 16, 17, 18.
  • Homework #3 (due on 09/18): 1.9 - 21, 22, 31(hard one!), 41.
  • Homework #4 (due on 09/25): 1.9 - 33(i), 34, 44; 2.6 - 1(b).
  • Homework #5 (due on 10/04): 2.6 - 3, 6, 7.
  • No homework due on Friday (Oct 11).
  • Homework #6 (due on 10/18): 2.6 - 9 (b) (d), 11, 19(a) (b) (c)
  • Homework #7 (due on 10/25): 2.6 - 19(d) (e), 27(a) (b); 3.4 - 2
  • Homework #8 (due on 11/01): 3.4 - 4, 5, 6, 17.
  • Homework #9 (due on 11/08): 3.4 - 18, 22; 4.6 - 1, 3.
  • Homework #10(due on 11/15): 4.6 - 8, 13, 17(a).
  • No homework due on Friday (Nov 22)
  • Homework #11(due on 12/02): 4.6 - 20, 24, 28;
  • Homework #12(No need to turn in): 5.10 - 5 (a), 6(a) (b) (d), 15, 22(a) (b), 28.(Solution)

Relevant Course Materials:

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