MA207-5-AU-CO:
Statistics II
PLEASE NOTE: This module is inactive. Visit the Module Directory to view modules and variants offered during the current academic year.
2023/24
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Inactive
Thursday 05 October 2023
Friday 15 December 2023
15
04 October 2018
Requisites for this module
MA108 or EC252 or IA155
(none)
(none)
(none)
(none)
After a brief period of revision, this module looks closely at the relations between the principal continuous distributions, using moment generating functions to determine some properties. The module then
considers confidence intervals and hypothesis tests in the context of the mean and variance of a distribution. After examining bivariate distributions the module ends by considering the principal methods for
estimation of unknown parameters. The module uses the R software environment for statistical computing and graphics.
On completion of the module students should be able to:
-Use tables of the t-, F-, and chi-squared distributions.
- Determine a moment generating function (mgf) and understand the
importance of the one-to-one correspondence between an mgf and a pdf.
- Understand the notions of Type I and Type II errors.
- Carry out hypothesis tests concerning means and variances.
- Determine confidence intervals for means, variances and differences
between means.
- Handle bivariate distributions, understanding the relations between
joint, marginal and conditional distributions.
- Determine maximum likelihood and least squares estimates of unknown
parameters.
- Determine maximum likelihood estimates of unknown parameters.
- Use R for the data analysis examples of the module.
Syllabus
REVISION
Descriptive statistics using R. Events and their probabilities. Conditional probability. Independence.
Discrete random variables: probability mass functions; Bernoulli trials; binomial distribution; hypergeometric distribution.
Continuous random variables: probability density functions (pdf); cumulative distribution function (cdf); normal distribution.
Use of tables. Standardization. Linear combinations of normal variables.
CONTINUOUS DISTRIBUTIONS
Gamma distribution family. Chi-squared (relation to normal). Exponential (relation to Poisson).
The t-distribution (Use of tables, relation to normal and chi-squared distributions).
The F-distribution (Use of tables, relation to t- and chi-squared distributions).
Moment Generating Functions.
Additivity of normal and chi-squared distributions.
Basic law of large numbers. Proof of central limit theorem.
CONFIDENCE INTERVALS AND HYPOTHESIS TESTS
Distributions of the sample mean and of the difference between means.
Null and alternative hypotheses. p-values. Type I and II errors. Power curve.
One-sided and two-sided tests for a population mean (variance known and unknown).
Hypotheses about means.
Distributions of the sample variance and of a ratio of two variances.
Hypotheses about variances.
Confidence interval for mean (known or normal and unknown) .
Confidence interval for a difference between means (known variances, or normal distribution with common variance).
Confidence interval for a variance.
BIVARIATE DISTRIBUTIONS
Bivariate discrete random variables; joint distributions; marginal distributions; independence; covariance and correlation;
Bivariate continuous distributions;
Bivariate normal distribution.
ESTIMATION - MAXIMUM LIKELIHOOD AND LEAST SQUARES
The method of maximum likelihood.
No information available.
No information available.
Available to Socrates /IP students spending all relevant terms at Essex.
The module has 27 contact hours in total. 2 lectures each week for 9 weeks, 1 lab in weeks 2-4 and 1 class in weeks 5-9 and 11, during the autumn term.
In the summer term 3 revision lectures are given. A project is undertaken in (about) 5-person groups.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Exam |
Main exam: In-Person, Open Book, 120 minutes during Summer (Main Period)
|
| Exam |
Reassessment Main exam: In-Person, Open Book, 120 minutes during September (Reassessment Period)
|
Additional coursework information
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Aris Perperoglou, email: aperpe@essex.ac.uk.
Dr Aris Perperoglou, email aperpe@essex.ac.uk
Miss Claire Watts, Department Manager, Tel. 01206 873040, email cmwatts@essex.ac.uk
Yes
Yes
No
No external examiner information available for this module.
Available via Moodle
Of 39 hours, 0 (0%) hours available to students:
6 hours not recorded due to service coverage or fault;
33 hours not recorded due to opt-out by lecturer(s).
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