Slides-05 - ECON1203/ECON2292 Business and Economic...

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Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 5
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22 Week 5 topics l Discrete probability distributions l Binomial distribution l Continuous probability distributions l Uniform distribution l Key references l Keller 7.4, 8.1
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Introduction to binomial distribution l Previously derived probability distributions from first principles l Recall distribution of males in gender composition example l But probability distribution of heads in 3 coin tosses has exactly the same distribution l Context of examples is different l But each of (three) ‘trials’ has one of two possible outcomes (male/female, or head/tail) l Generic distribution here is the binomial 33
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Introduction to binomial distribution… l Based on notion of a binomial experiment consisting of a sequence of trials l Assumptions for binomial experiment l Sequence of fixed number of n trials l Each trial has 2 outcomes, arbitrarily denoted success l Fixed probability of success (failure) p (1- p ) over trials l Trials are independent l Under these assumptions have a sequence of Bernoulli trials 44
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Binomial random variable l Have a sequence of Bernoulli rv’s l X 1, X 2, …, X n where X i = 1 if success & X i = 0 for a failure l Under assumptions made this is a sequence of independent & identically distributed (iid) rv’s l E.g. If n = 5 , one possible outcome of the sequence of trials is 0, 1, 1, 0, 1 l Another is 1, 1, 0, 0, 0 etc. 55
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Binomial random variable… l Often interested in rv’s constructed from other rv’s l Consider rv formed by summing these n Bernoulli rv’s l X = X 1 + X 2 + … + X n l X represents number of success in n trials & is called a binomial random variable l Characterized by 2 parameters n & p l Once we know the parameter values we know 66
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Binomial distribution l In gender composition example can calculate
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Slides-05 - ECON1203/ECON2292 Business and Economic...

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