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Test 2 Notes

Test 2 Notes - Test 2 Notes 5.1 How can probability...

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Test 2 Notes 5.1 How can probability quantify randomness? Probability gives us the foundation necessary to make inferences about the population of interest based on the information obtained from sample data. Probability of an event : the proportion of times the event is expected to occur in many repeated trials of a random phenomenon; p(event) o chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run o probability describes only what happens in the long run o probability=long-term RF the law of large numbers : as the number of repetitions of a random phenomenon increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome o it gets closer and closer to 50% the longer the study independent trials: different trials of a random phenomenon are independent if the outcome of any one trial is not affected by the outcome of any other trial Ex 5.6: consider a random number generator designed for equally likely outcomes. Which of the following is not correct, and why? o For each random digit generated, each integer between 0 and 9 has a probability of . 10 being selected o If you generate 10 random digits, each integer between 0 and 9 much occur exactly once o If you generated a very large number of random digits, then each integer between 0 and 9 would occur close to 10% of the time o The cumulative proportion of times that a 0 is generate tends to get closer to .10 as the number of random digits generated gets larger and larger 5.2 How can we find probabilities? Sample space(S): the set of all possible outcomes from a random phenomenon o Toss a fair coin: {H,T} o Roll a fair die:{1,2,3,4,5,6}

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Event: a subset of the sample space possessing a designated feature, events are denoted by capital letters o A-even {2,4,6} o B-odd {1,3,5} o C-5 {5} Tree diagram: tool used to determine the outcomes of a sample space o Example in notebook Probabilities for a sample space: o
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Test 2 Notes - Test 2 Notes 5.1 How can probability...

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