Examples and Problems in Mathematical Statistics

PART II: EXAMPLES

Example 1.1 We illustrate here two algebras.

The sample space is finite

Let E1 = {1, 2}, E2 = {9, 10}. The algebra generated by E1 and E2, 1, contains the events

The algebra generated by the partition = {E1, E2, E3, E4}, where E1 = {1, 2}, E2 = {9, 10}, E3 = {3, 4, 5}, E4 = {6, 7, 8} contains the 24 = 16 events

Notice that the complement of each set in 2 is in 2. 1 2. Also, 2 ().        

Example 1.2 In this example we consider a random walk on the integers. Consider an experiment ...