澳洲統(tǒng)計(jì)模型STAT2011課程作業(yè)輔導(dǎo)如果您打算主修數(shù)學(xué)，計(jì)算機(jī)科學(xué)或物理學(xué)，或者在悉尼大學(xué)攻讀工程課程，則需要對(duì)HSC Mathematics Extension 1(3單元)有很好的了解。

　　如果您已經(jīng)完成并對(duì)HSC數(shù)學(xué)有了很好的了解，并希望參加一門假定具有HSC數(shù)學(xué)擴(kuò)展1知識(shí)的課程，那么擴(kuò)展1橋梁課程就是為您準(zhǔn)備的。內(nèi)容將涵蓋我們?cè)跀?shù)學(xué)擴(kuò)展1中選擇的主題相信對(duì)學(xué)生最有利。有關(guān)內(nèi)容的詳細(xì)信息，請(qǐng)單擊此處。

　　統(tǒng)計(jì)模型STAT2011課程詳情

　　學(xué)生收到UAC的錄取通知后 ，擴(kuò)展1銜接課程將于2020年2月3日星期一開始。該課程將以兩種形式提供：日間課程和夜校。每個(gè)課程包括12個(gè)兩個(gè)小時(shí)的課程。

　　班級(jí)規(guī)模很小，因此學(xué)生可以得到最大程度的個(gè)人關(guān)注。在銜接課程中，預(yù)計(jì)學(xué)生每天至少要花費(fèi)兩個(gè)小時(shí)進(jìn)行私人學(xué)習(xí)和家庭作業(yè)。

　　盡管該課程是專門為幫助學(xué)生注冊(cè)悉尼大學(xué)第一年主流數(shù)學(xué)課程而設(shè)計(jì)的，但計(jì)劃注冊(cè)其他機(jī)構(gòu)的學(xué)生也可以參加。請(qǐng)注意，銜接課程沒有考試。

　　費(fèi)用

　　任一課程的費(fèi)用均為435美元。費(fèi)用包括商品及服務(wù)稅(GST)和小班授課的24小時(shí)學(xué)費(fèi)，一本帶簡(jiǎn)短筆記的練習(xí)本，以及每天在數(shù)學(xué)學(xué)習(xí)中心多花兩個(gè)小時(shí)的機(jī)會(huì)，那里可以提供個(gè)人幫助。填寫報(bào)名表(請(qǐng)參閱下文)時(shí)，必須使用信用卡(僅萬事達(dá)卡或Visa卡)支付費(fèi)用。報(bào)名和付款的截止日期為2020年1月30日(星期四)午夜。

　　日期和時(shí)間

　　課程日期天時(shí)報(bào)

　　擴(kuò)展1

　　(白天)2月3日星期一至2月18日星期二周一至周五上午10點(diǎn)至中午12點(diǎn)

　　分機(jī)1

　　(晚上)2月3日星期一至2月20日星期四周一至周四下午6點(diǎn)至晚上8點(diǎn)

　　去哪兒

　　所有學(xué)生應(yīng)于2020年2月3日星期一來到悉尼大學(xué)新法學(xué)院附樓研討會(huì)440室。新法學(xué)院附樓在化學(xué)學(xué)院對(duì)面的東部大街主校區(qū)。440室位于4樓。

　　白天的學(xué)生將從上午9:30開始分配課程，晚上的學(xué)生將從下午5:30開始分配課程。請(qǐng)確保您在課程于上午10:00(白天)和下午6:00(晚上)開始之前及時(shí)到達(dá)以完成此過程。

　　入學(xué)條件

　　大學(xué)保留在課程開始之前或期間更改銜接課程安排，取消或終止課程或拒絕法律允許的任何注冊(cè)的權(quán)利。如果任何課程的入學(xué)人數(shù)不足，大學(xué)保留向?qū)W生提供選擇其他安排或退款的權(quán)利。

　　如果您提前注冊(cè)并支付銜接課程費(fèi)用，但后來卻發(fā)現(xiàn)自己無法參加該課程，只要您在開課日期前至少一周告知我們，您的費(fèi)用將退還(減去25美元的管理費(fèi))。我們的聯(lián)系方式如下。請(qǐng)注意，大學(xué)對(duì)個(gè)人情況或工作承諾的任何變化不承擔(dān)任何責(zé)任。

　　隱私聲明：數(shù)學(xué)學(xué)習(xí)中心和悉尼大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院需要您在注冊(cè)表中提供的信息，以管理您的注冊(cè)和參加銜接課程。未經(jīng)您的明確同意，除非法律要求，否則任何個(gè)人信息都不會(huì)在大學(xué)之外泄露。

? ? ? Statistical Models STAT2011 Lecturer: Michael Stewart (Carslaw 818) Semester 1, 2017 Unit of Study Outline This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random variable models, like the binomial, Poisson and geometric, and continuous models, including the normal and exponential, will be studied. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. All students are expected to attend 3 lectures, 1 tutorial and 1 computer class per week. All room numbers are for the Carslaw building. ? Lectures: Monday, Tuesday and Wednesday in 175. ? Tutorials: Wednesday 2pm (453); Thursday 2pm (451,729/30,354) from week 2. ? Computer classes: Wednesday 3pm (705/6); Thursday 3pm (610/1,705/6,729/30) from week 2. For statistical computing we shall be using the RStudio graphical interface (freely available from rstudio.com) to the R statistical computing environment (freely available from r-project.org) for generating reports using the LATEX typesetting system (freely available from latex-project.org). Students are encouraged to install these three pieces of free, open source and cross-platform software on their own machines. Electronic communication Please send all emails to STAT2011@sydney.edu.au. Messages sent to any other address may not be responded to. Please include your name and student number in all communication and/or send from your official university email address. Assessment breakdown 1. Written examination: 65% 2. Quizzes (held in tutorial classes in weeks 4, 7 and 10): 15% 1 3. Computer test (held in the week 13 computer class): 10% 4. Weekly computer work (weeks 2–12): 10% Learning Outcomes 1. Construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models. such as probabilities, expectations and variances. 2. Fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters. 3. Compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates. 4. Assess the goodness of fit (as appropriate) of a fitted model. 5. [D] Apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory. 6. [HD] Prove certain mathematical results (e.g. inequalities, limiting results) used in the course. Approximately equal weight will be applied to each of these 6 outcomes in the overall assessment breakdown. A student will need to reach a basic level of competency in all of outcomes 1 to 4 to receive a passing grade. Certain tutorial exercises concerning material in outcomes 1 to 4 will go beyond “basic”; these will be marked with a star? . Tutorial exercises concerning outcomes 5 and 6 will be marked with D or HD as appropriate. Lecture schedule There are 3 lectures in each of the 13 weeks of semester (none are lost to public holidays) giving 39 lectures. Of these, 37 are scheduled with new material, the last two are left as review lectures. A draft schedule appears below with (a), (b) and (c) corresponding to Monday, Tuesday and Wednesday respectively. Lecture notes and other resources will be available at sydney.edu.au/science/maths/STAT2011. 1. (a) Introduction; overview; classical probability; revision; examples. (b) Simple/classical random variables; prob distribution; expectation; probability as expectation. (c) computational shortcut for expectation; functions of random variables; linear functions; variance; computational shortcut for E[g(X)]. 2. (a) Considering two random varibles at once; computational shortcut for E[g(X, Y )]. (b) Independence; V ar(X + Y ); covariance/correlation. (c) Combining experiments independently; urn models; sampling with replacement; models for each observation. 2 3. (a) E(Xˉ), V ar(Xˉ), E(S 2 ); binary case: full probability distribution of sum/mean. (b) Convergence in probability; Chebyshev’s inequality. (c) Proof of Chebyshev’s inequality using Markov’s inequality. 4. (a) Sampling without replacement; binary case: hypergeometric distribution including E(·) and V ar(·); E(·) and V ar(·) in the general case. (b) Serial No. model; order statistics. (c) Waiting time urn model; mean, variance; St Petersburg “paradox”. 5. (a) Assessing goodness of fit; Saxony data. (b) General binomial mixture models; two instances. (c) Conditional distributions; conditional expectation and variance formulae. 6. (a) ESTIMATION; modelling paradigm; measures of uncertainty. (b) Examples of unbiased estimators. (c) Biased estimators; Jensen’s inequality; waiting times example. 7. (a) Large sample approxmation to MSE; bootstrap methods. (b) Proof of convergence in probability of the secant gradient ratio. (c) Comparing estimators in the B(2, p) (genetics) example. 8. (a) The Cauchy-Schwartz inequality; Cramer-Rao lower bound; minimum variance unbiased estimators. (b) The method of maximum likelihood. Binomial example. (c) More maximum likelihood examples. 9. (a) Beyond classical probability; Poisson ; Geometric. (b) Negative binomial distribution. (c) Streams of events; Poisson counts; exponential waiting times. 10. (a) Cumulative distribution functions; probability density functions. (b) Continuous maximum likelihood; estimating exponential rate. (c) Gamma: integer shape; positive shape. 11. (a) Uniform distribution: limit of a single draw from Serial no. model. (b) Uniform sample as limit of Serial number model; order statistics; beta distribution. (c) Transforming from the uniform; large-sample approximations for general order statistics 12. (a) Graphical study of distributions of sums: (negative-)binomial, Poisson, gamma. (b) The normal distribution. The Central Limit Theorem. (c) Estimating a normal mean and variance. 13. (a) Assessing goodness of fit to the normal distribution; qq-plots; location/scale models. (b) Review of important examples. (c) Review of important examples. 3 Materials and Resources ? Lecture notes, tutorial and computer exercises and other materials will be made available via the course webpage: sydney.edu.au/science/maths/STAT2011 ? There is no formal textbook for the course, however the following references may be useful: – Statistics by David Freedman, Robert Pisani and Roger Purves (any edition). Possibly the best statistics textbook around, it emphasises concepts more than mathematics (it is designed for students without calculus). It used to be used in the now dormant unit STAT1021 General Statistical Methods (for Arts students) so several copies should be in the library. – An Introduction to Mathematical Statistics and Its Applications (any edition) by Richard J. Larsen and Morris L. Marx. This used to be a text for the course, it does not cover all of the current content, however it should be useful for basic concepts and procedures – there should be several copies in the library. – Mathematical Statistics and Data Analysis by John Rice. This is the text for STAT2911, is quite advanced but does cover some topics not covered by the Larsen and Marx book. – The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith. This elementary, fun book does a very good job of explaining tricky statistical concepts in an effective and entertaining way; very highly recommended (and quite inexpensive). Michael Stewart March 2017.