HC Maandag 09.00 - 10.45 in MIN 208; WC Maandag 11.00 - 12.45 in BBL 023 (blok 3) daarna BBL 161 (blok 4)

WISB262 Voortgezette Kansrekening

Textbook

A. Gut, An Intermediate Course of Probability, Springer, 2nd edition, 978-1-4419-0161-3

Evaluation

(i) Written homework assignments contribute up to 20% to the final grade The homework should be returned over the week before the next lecture, either in the class at the start of the lecture, or in the postbox in WG or per e-mail.

(ii) Midterm test contributes up to 40% to the final grade

(iii) Final exam 40%.

(iv) Herkansing.

  • 07.02 Material covered: Introduction Section 2, mathematical model of probability, sigma-algebras and their generators, the `coin-tossing' probability space, Borel sets, strong law of large numbers (overview).

    Homework problems

  • 14.02 Material covered: random variables (discrete and continuous), distribution, distribution function, probability (mass) function, density, gamma integral and gamma distribution, expected value as absolutely convergent integral/series

    Homework problems

  • 21.02 Material covered: pages 15-23; properties of the multivariate distribution functions, Borel sets in R^n, examples of multivariate r.v.'s with exponential marginals.

    Homework: Problems 1;8;14 (on pages 24-25).

    Problem: let (X,Y) be uniformly distributed in a disk, show that X and Y are uncorrelated

    (Each problem is worth 1 point. For electronic delivery: send solutions to Thom Klaasse [t.m.klaasse %AT% students.uu.nl])

  • 28.02 Material covered: pages 31-37, p. 40;

    Homework problems: 2.3 on page 35 , 2.5 on page 37, 8 on page 50, 2 on page 50, 16 on page 52. Each problem is worth 1 point.

  • 7.03 Material covered: pages 38-45 (+ Bayesian approach to prediction and estimation problems), Section 3.2 (stopped before Thm. 2.3)

    Homework problems: problems 30, 34 and 37 on pp. 54-55. Each problem is worth 1 point.

  • 21.03 Material covered: Ch. 3 Section 2, Ch. 3 Sections 6 and 7.

    Homework problems: Ch. 3 Section 8 problems 1, 22, 24, 37. Each problem is worth 1 point.

  • 28.03 Material covered: Continuity thm for generating functions, application to the Poisson approximation, Section 3.4 (to thm 4.9 but excluding thms 4.7, 4.8). p. 147 definition 1.4

    Homework problems: Ex. 4.1 p.73; Ex 4.2 p. 74, Ex. 4.5 p 76 (each 1 point)

    2-point problem: Let Y,Y_1,Y_2,... be discrete random variables with integer values. Show that Y_n converge in distribution (as n \to\infty) to Y if and only if the probability mass functions satisfy: p_{Y_n} (k) converge to p_Y (k) for every k

  • 04.04 Material covered: pp 74-77, Chapter 6 section 5, stable distributions and limits distributions for sums (overview),

    Homework problems: p. 92: problems 10,11,13; p. 178: 10(b)+(c); p. 180: 25. Each (sub)problem is worth 1 point.

  • 11.04 No lecture; Werkcollege starts at 11:00.
  • 02.05 Material covered: geometric construction of the bivariate standard normal; pp 117-126

    Homework problems: p. 140: problems 1,2,3,4; each worth one point

  • 09.05 Material covered: pp 127-135 (Thm 8.3 skipped), chi-square distribution

    Homework problems on p. 140 onwards: problems 12,15,24; and the problem:

    For A,B,C iid normal(0,1) random variables, Y := A^2 + B^2 + C^2 find the conditional distribution of Y given A+B+C=0.

    Each problem worth 1 point.

  • 16.05 Material covered: pp 147-155

    Homework problems on p. 158 Ex 3.2 and 3.3; p. 176 Ex 12

    Suppose P(X_n=0)=1-1/n, P(X_n= +n)=1/(2n), P(X_n= -n)=1/(2n). Determine if X_n converge to 0 in probability and/or in pth mean.

    Each problem worth 1 point.

  • 23.05 Material covered and Homework

  • 30.05 Herkansing (no lecture/exercises)
  • 6.06 Material covered: Order statistics pp. 101-113.
  • 20.06 studieweek: werkcollege at 11:00