Probability Theory: Homework 2
Exercises, due Wed Sept 17.
Jacod and Protter: 4.1, 5.20 and 7.11
4.1 (Poisson Approximation to the Binomial) Let be a Binomial probability with probability of success and the number of trials . Let . Show that
Let and let change so that remains constant. Conclude that for small and large ,
, where .
5.20 Suppose that takes its values in . Show that
7.11 Let for a nonnegative function with . Let , a singleton. Show that is a Borel set and also a null set (that is, ).