STATMODS[1] - MATH 1730 Introduction to Statistics 1...

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MATH 1730 Introduction to Statistics 1 Department: Statistics Semester: 1 No. of credits: 10 Level: 1 Prerequisites: A-level Mathematics, or equivalent. Programmes of Study: MMath; Mathematical Studies; Joint Honours (Science); Joint Honours (Arts); Mathematics with Finance. Aims: To provide an introduction to statistics. Objectives: On completion of this module, students should be able to: a) demonstrate foundation skills in statistical methods, including; b) descriptive statistics and methods of statistical inference. Methods of teaching: Hours: Lectures: 20 Tutorials: 0 Practicals: 3 Other Hours: 5 Examples Classes (joint with MATH 1750). Monitoring of progress: Marked exercises and assessed practicals. Outline Syllabus: Summarising data, graphs and summary statistics; probability and random variables, discrete and continuous; normal distribution; independent identically distributed random variables; confidence intervals and hypothesis tests for means. Detailed Syllabus: 1. Introduction. Applications. Types of data. Populations and samples. Frequency distributions. Histograms. 2. Measures of location. Measures of spread. Interpreting the standard deviation. Quartiles. Sample moments. 3. Probability and random variables. Probability rules. Independence. Random variables. Mean and variance of a discrete random variable. 4. Discrete distributions. Binomial and Poisson distributions. Poisson approximation to the Binomial. The Geometric distribution. Probability generating functions. 5. Continuous random variables. Cumulative distribution function. Probability density function. Mean and variance of a continuous random variable. Population Moments. 6. Continuous distributions. Exponential distribution. The Normal distribution. Use of tables. Normal approximation to Binomial. 7. Statistical Inference. Iid random variables. Point estimation. Sampling distribution of the sample mean. Central limit theorem. Interval estimation. Confidence intervals for mean (variance known and unknown). 8. Hypothesis testing for means. p-values. Tests concerning means. z-test. t-test. Booklist: 1. F. Daly, D. J. Hand, M. C. Jones, A. D. Lunn, K. J. McConway, Elements of Statistics, Addison-Wesley, 1995*. 2. D. G. Rees, Foundations of Statistics, Chapman and Hall, 1987. Informal Description: The subject of Statistics plays an increasingly important role in all our lives. Questions such as Does this drug work ?, Will this candidate be elected ?, Is product A of better quality than product B ?, Will this flood defence work ?, can all be answered by statistical analysis. This course provides an introduction to the essential elements of Statistics. We shall first consider descriptive statistics for data summary, including graphical and numerical techniques. The key ideas of probability and random variables are then discussed, including the Binomial, Poisson, Exponential and Normal distributions. Finally, in order to answer questions such as those above, we introduce statistical

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