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Examples and Problems in Mathematical Statistics by Shelemyahu Zacks

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PART II: EXAMPLES

Example 1.1 We illustrate here two algebras.

The sample space is finite

Unnumbered Display Equation

Let E1 = {1, 2}, E2 = {9, 10}. The algebra generated by E1 and E2, inline1, contains the events

Unnumbered Display Equation

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

Unnumbered Display Equation

Notice that the complement of each set in inline2 is in inline2. inline1 inline inline2. Also, 2 ().        

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

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