01.-intro-sets-axioms

01.-intro-sets-axioms - Summary Examples Example 1 An...

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Summary Examples Example 1 An experiment consists of tossing a die and then flipping a coin once if the die outcome is even. If the die outcome is odd, the coin is flipped twice. a) Describe the sample space by listing its elements. b) Describe the sample space using a tree diagram. Answer: a) S = {(1HH), (1HT), (1TH), (1TT), (2H), (2T), (3HH), (3HT), (3TH), (3TT), (4H), (4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)} b) Example 2 For the sample in example 1: a) list the elements of event A: a number less than 3 occurs on the die A = {(1HH), (1HT), (1TH), (1TT), (2H), (2T)} b) list the elements of event B: two tails occur B = {(1TT), (3TT), (5TT)} c) list the elements of event A A = {(3HH), (3HT), (3TH), (3TT), (4H), (4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)} d) list the elements of event A ′∩ B A ′∩ B = {(3TT), (5TT)} e) list the elements of event A B 4 H T 6 H T 2 H T 1 H T H T H T 3 H T H T H T 5 H T H T H T
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A B = {(1HH), (1HT), (1TH), (1TT), (2H), (2T), (3TT), (5TT)} Example 3 Let S = {x|0<x<12} M = {x|1<x<9} and N= {x|0<x<5}. Find: (What is x? real number? Integer? DOES IT MATTER?) a) M N = { x | 0 < x < 9 } b) M N = { x | 1 < x < 5 } c) M = { x | 9 x < 12 }, N = { x | 5 x < 12 } M ′∩ N = { x | 9 x < 12 } Probability I suspect that most students have a good intuitive concept for what probability is. It represents in some sense the "likelihood" or the "chance" or the "odds" that something (some event) will happen as the result of an experiment. For example you would probably agree with a model which specifies that the probability a flipped coin will come up a head is 0.5. This is the same as saying the odds are 1 to 1 that a head will come up, or that there is a 50% chance of a head. Similarly, a model specifying the probability of rolling a die and getting a 6 is 1/6 (5 to 1 odds against, 16.666% chance). It should be made clear that probabilities are associated with events. That is; "What has a
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This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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01.-intro-sets-axioms - Summary Examples Example 1 An...

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