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”

# Category Archives: Probability Theory

## 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”

## Welcome to Probability and Measure Theory

In our first class we asked the question “What is randomness?” and started thinking about the Axiomatic Foundation of Probability. More details to come …