Homework 4, due Friday Oct 24

Jacod and Protter, problems 11.5, 12.4 and 12.11 11.15 Let be a continuous distribution function and the  be uniform on . Define . Show that has distribution function . 12.4 Let denote the correlation coefficient for . Let , and . Show that . (This is useful because it shows that is independent of theContinue reading “Homework 4, due Friday Oct 24”

Probability Theory, Homework 3, due Friday Oct 3.

From Jacod and Protter 9.5  Let be a probability space. Suppose that is a random variable with almost surely and . Define by . Show that defines a probability measure on . 9.7 Suppose that and let be defined as above. Let denote expectation with respect to .  Show that . Further exercises Exercise 3.Continue reading “Probability Theory, Homework 3, due Friday Oct 3.”

Probability Theory: Homework 1

Exercises, due Wed Sept 3. From Jacod and Protter, problems 2.6, 2.7, 2.10 and 2.14. 2.6 Let be a -algebra of subsets of and let . Show that is a -algebra of subsets of .  Is this still true if is a subset of that is not a member of ? 2.7  Let be aContinue reading “Probability Theory: Homework 1”