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MAT 521Spring Lecture 2

MAT 521Spring Lecture 2 - Lecture 2 Section 1.6 Finite...

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Lecture 2 Section 1.6: Finite Sample Spaces A Finite Sample Space is a sample space with a finite number of outcomes. Let S be a finite sample space containing elements s 1 , s 2 , …, s n . The probability distribution on S is specified by assigning a probability p i to each point s i S (i = 1, 2, …, n.) In order to satisfy the axioms for a probability distribution, the numbers p 1 , p 2 , …, p n must satisfy the two conditions: (1) p i 0 for i = 1, 2, …, n and (2) i p n 1 i = Σ = 1. A Simple Sample Space is called a simple sample space if all the n elements in the sample space have the same probability p i = 1/n (i = 1, 2, …, n.)

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If an event A in a n-elements simple sample space contains m elements, then Pr(A) = m/n. Example: Toss a fair coin three times. Describe the sample space and give the probability on each element in the sample space. Example 1.6.4 Roll two fair dice once. Describe the sample space and give the probability on each element in the sample space. Practice Problems:
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MAT 521Spring Lecture 2 - Lecture 2 Section 1.6 Finite...

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