chapt2 - Chapter 2: Probability 2.1 Sample Spaces and...

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Chapter 2: Probability 2.1 Sample Spaces and Events experiment – action or process that generates observations (Example: Select two cards at random (with replacement) from a standard deck and observe the suit.) sample space (of an experiment) – set of all possible outcomes of that experiment, denoted by S What are some possible outcomes to my experiment? How many outcomes are possible? event – collection (subset) of outcomes simple – consists of exactly one outcome compound – consists of more than one outcome Let A = the first card is a heart and let B = the second card is a spade. union (of two events A and B) – all outcomes that are either in A or in B or in both events, denoted by ______________ What outcomes are in the union of A and B? intersection (of events A and B) – all outcomes that are in both A and B, denoted by ______________ What outcomes are in the intersection of A and B? Page 1 of 9
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complement (of event A) – all outcomes in S not in A, denoted by A’ Two events are mutually exclusive or disjoint if they have no outcomes in common. Can you think of two events from the card example above that are disjoint? 2.2 Axioms, Interpretations, and Properties of Probability Objective of Probability: Assign each event A a number P(A), called the probability of the event A, which will give a precise measure of the chance that A will occur. Axioms Axiom 1: P(A) ≥ 0 Axiom 2: P( S ) = 1 Axiom 3: a. If A 1 , A 2 , …, A k is a finite collection of mutually exclusive events, then P(A 1 – A 2 – …– A k ) = = k i 1 P(A i ) b. If A 1 , A 2 , A 3 ,… is an infinite collection of mutually exclusive events, then P(A 1 – A 2 – A 3 …) = = 1 i P(A i ) Page 2 of 9
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Interpretations relative frequency – if we perform the experiment repeatedly, P(A) is proportion of the replications for which event A will occur In our playing card example, A = the event that the first card selected is a heart. What is P(A)? ______ Thus, if we performed this experiment over and over again, we expect that in about 1 out of every _____ experiments we perform, the first card pulled will be a heart. Consider an experiment consisting of one flip of a coin.
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This note was uploaded on 03/18/2008 for the course STAT 401 taught by Professor Akritas during the Spring '00 term at Pennsylvania State University, University Park.

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chapt2 - Chapter 2: Probability 2.1 Sample Spaces and...

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