Slides-04 - ECON1203/ECON2292 Business and Economic...

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Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 4
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22 Week 4 topics l Random variables l Discrete probability distributions l Mathematical expectation l Key references l Keller 7.1-7.4
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33 Random variables l Definition: A function that assigns a real number to each point in the sample space l SIA: Private health insurance l PHI = 1 if have private health insurance PHI = 0 if don’t have private health insurance l Example of a discrete random variable (rv) l It is a Bernoulli or indicator rv l A different rv might be Y = length of time since first took out Private health insurance l Example of a continuous rv
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Random variables… l Another example of a continuous rv would be l X = age of student randomly selected from class l Will distinguish between the rv, say, X & particular values taken by the rv, say x l So, X is the named random variable & x a realized value thereof l Then want to calculate associated probabilities l P ( X = x ) or that P ( X < x ) 44
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55 Gender composition l Suppose interested in gender composition in families l Define X = number of boys in families with 3 children l Thus X = 0, 1, 2 or 3 l Assume l Births are independent events l Males & females are equally likely to be born l What is the probability distribution of X ? l Have determined outcomes so now need to calculate associated probabilities
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66 Gender composition… l Note l Could have used a probability tree to isolate the 8 outcomes & associated probabilities l Resultant probability distribution satisfies l P ( X = x ) ≥ 0 for all x & = = x x X P all 1 ) (
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77 Gender composition… l Can also represent distributions in terms of the cumulative distribution function (cdf) l Defined as F ( x ) = P ( X x ) for all x
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88 Gender composition… l A probability distribution (or cdf) can be used to determine probabilities l What is P (0 < X < 3)?
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