Assignment - Mathematics
Measure Theory:
1. Let X be a set with four elements. How many algebras of subsets of X are there that contain exactly (a) four subsets? (b) five subsets? You must explain your answers carefully.
2. Write each of the following events in Bernoulli Space in terms of the simple events
En. (Reminder: En = {? ? ? : ?n = 1}, the event that the nth toss is Heads.)
(a) We get exactly two Heads (no more, no less.)
(b) The sequence THT never appears.
3. Give a verbal description of the following events in Bernoulli space:
(a) 3. Give a verbal description of the following events in Bernoulli space: