Weeks 9 & 10 Notes (Chapters 17 & 18)
Weeks 9 & 10 Notes (Chapters 17 & 18) STAT 1350 Intro to Stats
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This 2 page Class Notes was uploaded by Katie Catipon on Tuesday March 24, 2015. The Class Notes belongs to STAT 1350 Intro to Stats at Ohio State University taught by Alice Miller in Spring2015. Since its upload, it has received 154 views. For similar materials see Intro to Stats in Statistics at Ohio State University.
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Date Created: 03/24/15
Chapter 17 Thinking about Chance Chance behavior in the short run unpredictable Chance behavior in the long run regular and predictable pattern Random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions Probability any outcome of a random phenomenon is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions Probability 05 means occurs half the time in a very large number of trails Outcome with probability 0 never occurs Outcome with probability 1 happens on every repetition quotLaw of averagesquot aka Law of large numbers states that in a large number of independent implying that knowing the outcome of one trial does not change the probabilities for the outcomes of any other trials the trials have no memories repetitions of a random phenomenon averagesmeans or proportions are likely to become more stable as the number of trials increases whereas sums or counts are likely to become more variable Personal Probability a number between 0 and 1 that expresses and individual s judgment of how likely the outcome is Advantage aren t limited to repeatable settings Useful because we base decisions on them They are opinions thus cannot be said to be right or wrong Note Probability in terms of quotpersonal judgment of how likely and probability in terms of quotwhat happens in many repetitions are two completely different ideas They are not two explanations of the same thing Chapter 18 Probability Models Probability model in terms of a random phenomenon describes all the possible outcomes and says how to assign probabilities to any collection of outcomes We sometimes call the collection of outcomes an event 0 Rules that all probability models must obey 1 Any probability is a number between 0 and 1 because any proportion is a number between 0 and 1 2 All possible outcomes together must equal probability 1 3 The probability that an event does not occur 1 the probability that the event does occur 4 If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities A probability is incoherent when it does not follow rules 1 amp 2 They don t go together in a way that makes sense Sampling distribution in terms of a statistic tells us what values the statistic tales in repeated samples from the same population and how often it takes those values We think of a sampling distribution as assigning probabilities to the values the statistic can take Because there are usually many possible values sampling distributions are often described by a density curve such as a Normal curve