exampleSet2

ExampleSet2 - More Sample Spaces and Set Notation Examples Example 1 Roll 2 dies one after the other and record the roll of the rst die and then

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More Sample Spaces and Set Notation Examples Example 1 Roll 2 dies, one after the other, and record the roll of the Frst die and then the roll of the second die, a possible outcome is an ordered pair of two numbers and the sample space is Ω 1 = (1 , 1) , (1 , 2) ... (1 , 6) (2 , 1) , (2 , 2) ... (2 , 6) . . . . . . . . . . . . (6 , 1) , (6 , 2) ... (6 , 6) ±or this sample space, the order of the rolls matters - this gives us 36 elementary events, all of which have the same probability of occurring. Example 2 Alternatively, we could just record the outcomes of rolling the two dies at the same time. An outcome then has the form of a set of two numbers (in a set, the order of the elements does not matter, i.e. we can re-arrange them freely). This leads us to a slightly di²erent sample space: Ω 2 = { 1 , 1 } , { 1 , 2 } ... { 1 , 6 } { 2 , 2 } ... { 2 , 6 } . .

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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

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ExampleSet2 - More Sample Spaces and Set Notation Examples Example 1 Roll 2 dies one after the other and record the roll of the rst die and then

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