Slides-06

Slides-06 - ECON1203/ECON2292 Business and Economic...

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Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 6
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22 Week 6 topics l Normal distribution l Calculating areas under the normal curve l Normal approximation to the Binomial l Concept of an estimator l Properties of estimators l Key references l Keller 8.2, 9.2 pp 309-314, 10.1
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Normal distribution l l In practice heights of men & women are well- approximated by normal distributions l Will play a prominent role in upcoming discussion of statistical inference l It is a continuous rv l P ( X = x ) = 0 l l Completely characterized by its mean μ & variance σ 2 33
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Normal distribution… l Graphically, the probability density function (pdf) l l mean=median=mode l Basic features include l Range of “support” is unlimited, so ∞ ≤ x ≤ ∞ l Despite unlimited range little area in tails of a normal distribution l 4.6% outside μ ±2 σ ; 0.3% outside ±3 (confirm from tables) l Relevant tables in Keller,Table 3, p. B8-B9 l Also Part II of tutorial program 44
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55 Normal distribution …
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66 Normal distribution … l If X is normally distributed with mean μ and variance σ 2 then we write l X ~ N ( , 2) l Algebraic formula for pdf of a normal rv
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77 Normal distribution … l No “rules” for when normal distribution is appropriate l l Theoretical reasons why the normal is useful in problems involving samples from other populations l Can also use statistical methods to assess whether a normal “model” might be reasonable l Refer Week 12
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Normal distribution as a model l How can heights be normally distributed when negative heights aren’t possible? l Let X be heights of 2 year olds in cms & assume X ~ N (80, 16) l How far is zero from mean of X ? l
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Slides-06 - ECON1203/ECON2292 Business and Economic...

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