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Lecture "Probability & statistics - Chapter 8: Estimation" has contents: Concept of estimate, point estimate, maximum likelihood estimate, interval estimate, for mean, for proportion, for variance. Invite you to consult the content. | Lecture Probability & statistics: Chapter 8 - Bùi Dương Hải Lecture 8. ESTIMATION [1] Chapter 8, Chapter 11 Concept of Estimate Point Estimate Maximum Likelihood Estimate Interval Estimate For Mean For Proportion For Variance (pp. 484 – 488) PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 1 8.1. Concept of Estimate Estimation is determining the approximate value of a unknown parameter on given data. Two types of estimate: Point estimate: single value Interval estimate: an interval that parameter falls into it with a determined probability level Ex. “The average height of VN’s male is 163 cm” “The average height of VN’s male is from 160 to 165 cm” PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 2 8.2. Point Estimate Point estimate of parameter is denoted by Estimator: a statistic calculated on random sample, an approximation to unknown parameter. Estimator is a random variable Estimate: specific value calculated on observed sample. Estimate is number. ∑ Ex. Formula ̅ = is an estimator Value ̅ = = 5 is an estimate PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 3 Point Estimate Population parameters , , are unknown Estimate by statistics from sample Sample mean ̅ is point estimate for Sample variance is point estimate for Sample proportion ̅ is point estimate for PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 4 Properties of Point Estimate Estimate for by Unbiased: is unbiased estimator of = Efficient: and are unbiased, is more efficient than : < If is smallest in every unbiased estimator: most efficient, best estimator BUE (Best Unbiased Estimator) PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 5 Example Example.8.1. Population mean , sample ( , , , ) (a)
