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Chapter 8

ECO220Y1 Chapter 8 Notes

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Jennifer Murdock

ECO220Y1 Textbook Notes Chapter 8 Randomness and Probability 81 Random Phenomena and Empirical ProbabilityRandom phenomenon a phenomenon is random if we know what outcomes could happen but not which particular values will happen o Ie whatof customers will call that qualify for the platinum cardTrial a single attempt or realization of a random phenomenon o Ie each call receivedOutcome the outcome of a trial is the value measured observed or reported for an individual instance of that trial o Ie either they qualify or they dontEvent a collection of outcomes Usually we identify events so that we can attach probabilities to them We denote events with bold capital letters such as A B or CSample space the collection of all possible outcome values It has a probability of 1 o It is denoted as S o Ie SQ N when looking at the calls SQQ QN NQ NN when looking at two calls togetherProbability a number between 0 and 1 that reports the likelihood of an events occurrence We write PA for the probability of event AEmpirical probability when the probability comes from the longrun relative frequency of the events occurrence it is an empirical probability o Ie in the long run the probability of a caller qualifying was 35Independence informally two events are independent if the fact that one event occurs does not change the probability of the otherIndependence formally Events A and B are independent when PBAPB or when PABPALaw of Large Numbers LLN the LLN states that the longrun relative frequency of repeated independent events settles down to the true relative frequency as the number of trials increases o Ie asof callsthe relative frequency settled to 35We can write Pqualified03582 The Nonexistent Law of AveragesThe law of averages is a belief that things have to even out in the short run o Ie the hitter has struck out 6 times in a row so he is due to hit the next time o This law does not existRelative frequencies even out only in the long run o Large in the LLN means infinitely largeOr in other words the long run is really long83 Two More Types of Probability
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