ECO220Y1 Lecture Notes - Lecture 7: Sampling Error, Sample Space, Randomness
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ECO220Y1 Full Course Notes
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Law of large numbers: very large samples will be highly representative of population from which they are drawn. Law of small numbers does not exist: is human bias, outcomes over short term are not representative of long term. Probability basis of inference: inferences about parameters use statistics affected by sampling noise, sample space, random experiment. Process that leads to one of several possible outcomes. S = {o1, o2, , ok} Mutually exclusive: lists all possible outcomes, can only be one outcome, event, probabilities. Interpret relative to infinite repetitions of random experiment. If outcomes mutually exclusive and exhaustive: probabilities between 0 and 1, add up to 1, complement. Event that occurs when a doesn"t occur: ac (or a", p(a) + p(a") = 1. Three types of probabilities: joint, marginal, conditional. If outcome mutually exclusive, add all joint probabilities with single event. P(a|b) = p(a and b) / p(b) One event is not affected by occurrence of another.
