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MATH 1730
Introduction to Statistics 1
Department: Statistics
Semester:
1
No. of credits: 10 Level: 1
Prerequisites:
Alevel 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.
pvalues. Tests concerning means. ztest. ttest.
Booklist:
1.
F. Daly, D. J. Hand, M. C. Jones, A. D. Lunn, K. J. McConway, Elements of Statistics, AddisonWesley,
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
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 Winter '07
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