STK4050 - Autumn 2011

Exercises for STK4050 Fall 2011

Reference are to the course text book R&K (Rubinstein & Kroese) unless otherwise stated.

Exercises for Monday 7/11:

From Home exam 2007: Exercises 4

From Exam 2009: Exercise 2

Try also to implement the methods in R.

Exercise 6.12 in R&K

Many of the other exercises from Chapter 6 are relevant, but 6.8-6.11 and 6.15-6.21 are not so central to the course.

Here is R-code for Problem 4 for Exam 2007, Problem 2 for Exam 2009, Exercise 6.12 and for Example 6.8 from R&K.

Exercises for Monday 31/10:

From 2007 (Hjort): Exercises 14 and the rest of 16 (leftovers)

From 2005 (Storvik): Exercise 20 (also leftover)

Exercise 6.6 in R&K

Here is R code for Exercise 14, R code and a figurefor the remainder of Exercise 16, R code for Exercise 20 and R code for Exercise 6.6.

Exercises for Monday 24/10:

From 2007 (Hjort): Exercises 14 and 16 minus question f)

Here is R code for Exercise 16.

From 2005 (Storvik): Exercises 19 (minus questions d) and e)) and 20

Here is R code for Exercise 19.

Exercises for Monday 17/10:

From 2007 (Hjort): 13 and 15

Here is R code for Exercise 15.

Exercises for Monday 10/10:

From 2007 (Hjort): 10 and 12

Here is some R-code for Ex. 10 , Ex. 12 .

For Exercise 12 the script produces somewhat different numbers from what we saw Monday since I had forgotten a "byrow=T" when making the simulated sequence a matrix.

Exercises for Monday 3/10:

Leftover: Exercises 10 in 2005-exercises (Storvik).

From R&K: 5.1, 5.7a, 5.8 and 5.14

More 2005-exercises (Storvik): 11 and 12 (note that we have done something similar to 12 in the lectures)

2007-exercise (Hjort) no. 1.

Here is some R-code for Ex. 10 , Ex. 11 , Ex. 12 from 2005, and for Ex. RK 5.14 and Ex. 1 from 2007.

Furthermore, here is the argument we omitted from RK 5.1 showing that with monotonic functions H(x) we have negative covariance betweeen H(X) and H(X') where X' is the antithetic variable to X.

Exercises for Monday 26/9:

Leftover from exercises 12/9: 2.22 and 2.23 in R&K

Exercises 5.6 (prove also E[Y]=E[E[Y|X]]) and 5.9 in R&K

Exercises 10 in 2005-exercises (Storvik).

Exercises for Monday 12/9:

Exercises 2.11, 2.12, 2.15, 2.19, 2.22, 2.23 in R&K

Exercises 5 in 2005-exercises (Storvik). (Here is an R-scripts for Ex.5, 2005 and Ex. 4, 2007).

Exercises 4 and 7 i 2007-exercises (Hjort) (An R-scripts for Ex.7, 2007).

Exercises for Monday 5/9:

Exercises 2.1-2.7 in K&L (2.1 and 2.3 already done in lecture Monday 29/8)

Exercises 1-4 in 2005-exercises (Storvik)

Exercises 5 and 6 i 2007-exercises (Hjort)

Hints and solutions for exercises 1, 2, 3, 4 from 2005-exercises and 5 and 6 from 2007-exercises.

Ansvarlig: Sven Ove Samuelsen. Oppdatert 27.09.11