Statistics Prelim 2 - 10:57:00 PM Statistics Prelim 2 Chapter 14 A phenomenon consists of trials Each trial has an outcome Outcomes combine to make

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31/03/2008 21:57:00 Statistics Prelim 2 Chapter 14 A phenomenon consists of trials. Each trial has an outcome. Outcomes combine to make events. The combination of all possible outcomes is the sample space As you collect more data, the outcomes becomes smaller and smaller fraction of accumulated experiences, so in the long fun the probability settles out Law of Large Numbers o If we assume that events are independent, and the outcome of one trial does not affect the outcome of the others, the LLN saws that as the number of trials increases, the long-run relative frequency of repeated events gets closer and closer to a single number o Called probability of an event o Because the definition is based on repeatedly observing the event’s outcome, this definition of probability is often called empirical probability. o Deals with the long run not the short run No Law of Averages that promises short-term compensation for recent deviations from expected behavior. When outcomes are equally likely, it is just 1 divided by the number of possible outcomes P(A) = # outcomes in A / # of possible outcomes We use the language of probability in everyday speech to express a degree of uncertainty without basing it on long run relative frequencies or mathematical models, this is known as personal probability Three rules for working with probability – Make a picture (3x) Rules of Probability o 1.) A probability is a number between 0 and 1 o 2.) Probability assignment rule – the set of all possible outcomes of a trial must have the probability of 1, P(S) = 1 o 3.) Complement Rule – the probability of an event occurring is 1 – the probability that it doesn’t occur, P(A) = 1 – P(Ac)
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o 4.) Addition Rule – for two disjoint events A and B, the probability that one or the other occurs is the sum of the probability of the two event P(A or B) = P(A) + P(B), provided the events are disjoint o Disjoint: no outcomes in common, mutually exclusive o 5.) Multiplication Rule: For two independent events A and B, the probability that both A and B occur is the product of the possibilities of the two events P(A and B) = P(A) x P(B), provided that the two events are independent o Independent: knowing whether one event occurs does not alter the probability that another even occurs The phrase “at least” is often a tip-off to think about the complement. Something that happens at least once is the complements of something not happening Independence Assumption: It’s unlikely that the choice made by one respondent affected the choice on another WHAT CAN GO WRONG o Beware of probabilities that don’t add up to 1 o Don’t add probabilities of events of they are not disjoint o Don’t multiply probabilities of events of they are not independent. o
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This note was uploaded on 05/09/2008 for the course ILRST 2100 taught by Professor Vellemanp during the Spring '07 term at Cornell University (Engineering School).

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Statistics Prelim 2 - 10:57:00 PM Statistics Prelim 2 Chapter 14 A phenomenon consists of trials Each trial has an outcome Outcomes combine to make

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