Chapter_10 - STAT 2053 Elementary Statistics Chapter 10...

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STAT 2053 – Elementary Statistics Chapter 10 – Introducing Probability
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2 Idea of Probability Probability is the science of chance behavior Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run this is why we can use probability to gain useful results from random samples and randomized comparative experiments Chapter 10
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Probability Theory In other words, for any random phenomenon, the results for a small number of repetitions are unpredictable. But for a large number of repetitions we can predict what the distribution of our results will look like. 3 Chapter 10
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4 Randomness and Probability Random : individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions Relative frequency (proportion of occurrences) of an outcome settles down to one value over the long run. That one value is then defined to be the probability of that outcome. The shorthand for probability is P(outcome). Chapter 10
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Probability Theory Example : When we toss a coin, there are two possible outcomes (heads or tails). If I toss a coin several times, about what percentage of these tosses should result in heads? Therefore, we say that the probability of flipping a coin and landing on heads is: 5 Chapter 10
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Probability Theory Example : HOWEVER, suppose I toss the coin 10 times: Am I going to get 5 heads every time I flip the coin 10 times? The idea of probability is that, as I toss the coin more and more times, the percentage of heads I get will get closer and closer to 50%. Variation, however, will cause that percentage in the short run to fluctuate (sometimes heavily). 6 Chapter 10
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Probability Theory Example : If A has the following probability, how often will A occur? (Never, Rarely, Very Often, or Everytime) .95 (or 95%): 0 (or 0%): 1 (or 100%): 0.001 (or 0.1%): Fact : The larger the probability of an outcome, the more likely we will observe that outcome. 7 Chapter 10
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8 Relative-Frequency Probabilities Can be determined (or checked) by observing a long series of independent trials (empirical data) experience with many samples simulation (computers, random number tables) Chapter 10
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9 Relative-Frequency Probabilities Coin flipping: Chapter 10
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10 Probability Models The sample space S of a random phenomenon is the set of all possible outcomes. An event is an outcome or a set of outcomes (subset of the sample space). A probability model is a mathematical description of long-run regularity consisting of a sample space S and a way of assigning probabilities to events. Chapter 10
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Sample Space Definition : For any random phenomenon, the sample space (denoted S) is the set of all possible outcomes for that phenomenon. Example
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Chapter_10 - STAT 2053 Elementary Statistics Chapter 10...

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