lecture33 - Lecture 32 Discrete Probability Sections 6.1...

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Lecture 32 Discrete Probability Sections 6.1 6.2
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Terminology Experiment: a procedure (which usually involves randomness) that yields an outcome (e.g. rolling a die) Sample space: the set of all possible outcomes (e.g. {1,2,3,4,5,6}) Event: a subset of the sample space (e.g. the die is even, or {2,4,6})
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Probability Given sample space S, we assign a number p(s) to each outcome s S such that p is a function from S to [0 1] and called a probability distribution. S s s p S s s p 1 ) ( each for 1 ) ( 0
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Event probabilities Recall that an event E is a subset of S, the sample space. Probability of E is the sum of the probabilities of the outcomes in E E s s p E p ) ( ) (
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Uniform distribution Each outcome has the same probability 1/|S| Example: (unbiased) coin toss S = {H,T} p(H) = ½, p(T) = ½ Example: rolling an unbiased die S = {1,2,3,4,5,6} p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
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Sampling with and without replacement An urn contains 3 blue balls and 5 red balls We pick a ball, put it away, pick another ball. What is the probability of picking
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This note was uploaded on 10/21/2011 for the course CSCI 2011 taught by Professor Staff during the Spring '08 term at Minnesota.

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lecture33 - Lecture 32 Discrete Probability Sections 6.1...

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