MA108-4-SP-CO:
Statistics I
2015/16
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 4
Current
15
-
Requisites for this module
(none)
(none)
(none)
EC114
EC252, MA216, MA225, MA318, MA319, MA322
BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC LG11 Economics and Mathematics,
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN1H Finance and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC GCF3 Mathematics with Physics (Including Year Abroad),
BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)
This course introduces students to the basic ideas of probability (combinatorial analysis and axioms of probability), conditional probability and independence, probability distributions and provides introductions to the handling data using descriptive statistics. The course uses R software package to clarify and illustrate theoretical concepts of probability, to show how random variables are generated and how they vary, to know how to construct appropriate diagrams for data summary.
Syllabus
Descriptive statistics:
Data collection and summary. Stem/leaf plots and histograms. Measures of location (Mode, median, mean).
Measures of spread. Quartiles. Box plots. Variance and standard deviation. Transformations.
Probability:
Relative frequency. Probability as a limit. Events. Union and intersection. Addition rule. Exclusive events. Independent events. Multiplication rule.
Permutations and combinations.
Conditional probability. Total probability theorem, Bayes' theorem.
Discrete probability distributions:
Discrete random variables. Probability distributions. Expectation. Algebra of expectations.
Variance. Bernoulli distribution. Binomial distribution (sampling with replacement).
Mean and variance of Bernoulli and binomial.
Poisson distribution (and applications).
Derivation of the Poisson. Approximation to the binomial.
Continuous probability distributions:
Density function as limit of histograms. Properties of probability density function (pdf). Cumulative distribution function (cdf). Uniform and exponential distribution. Expectations. Variance. Median, mode. Distributions of functions of random variables; change of variables formula.
Normal distribution. Use of tables. Central limit theorem. Additivity.
Moment generating function;
On completion of the course students should be able to:
- understand how to calculate and interpret simple summary statistics;
- how to choose and construct appropriate diagrams to illustrate data sets;
- use R for the data analysis examples of the course;
- understand and apply the addition rule and multiplication rule of probability;
- understand the basic ideas of conditional probability including the application of the total probability theorem and Bayes' theorem;
- understand and recognise situations appropriate for Binomial and Poisson models;
- calculate expectations and variances for discrete and continuous random variables, understand the ideas of probability density function and the distribution function;
- understand the change of variables formula and know how to calculate the distributions of functions of random variables
- understand moment generating functions
- recognise the central role of the normal distribution, be able to reduce normal random variables to standard form and be able to use tables of normal probabilities;
- understand the basic ideas of central limit theorem.
No information available.
No information available.
'A' level Maths or equivalent normally required. Available independently to Socrates/IP students spending all relevant terms at Essex.
This course consists of 30 contact hours consisting of 20 lectures and 10 classes. Coursework consists of 4 pieces of homework. There are three revision lectures in the summer term.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Homework 1 |
|
25% |
| Coursework |
Homework 2 |
|
25% |
| Coursework |
Homework 3 |
|
25% |
| Coursework |
Homework 4 |
|
25% |
| Exam |
Main exam: 90 minutes during Summer (Main 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 Martin Griffiths, email: maths@essex.ac.uk
Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email cmwatts@essex.ac.uk
Yes
No
No
No external examiner information available for this module.
Available via Moodle
No lecture recording information available for this module.
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