MA108-4-SP-CO:
Statistics I
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 4
Current
Sunday 17 January 2021
Friday 26 March 2021
15
21 February 2022
Requisites for this module
(none)
(none)
(none)
EC114
EC252, MA200, MA216, MA225, MA314, 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 L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1G3 Economics with Mathematics (Including Placement Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
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),
MSCIN399 Actuarial Science and Data Science,
MSCIG199 Mathematics and Data Science
For students outside of the Department, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure whether you meet this criteria please contact mathsug@essex.ac.uk before attempting to enrol.
This module introduces students to the basic ideas of probability (combinatorial analysis and axioms of probability), conditional probability and independence, probability distributions, and provides an introduction to handling data using descriptive statistics. This module uses the R software package to clarify and illustrate theoretical concepts of probability, to show how random variables are generated and how they vary, enabling the construction of appropriate diagrams for data summary. This module covers part of the CS1 IFOA syllabus.
No information available.
On completion of this module students should be able to:
1. understand how to calculate and interpret simple summary statistics;
2. how to choose and construct appropriate diagrams to illustrate data sets;
3. use R for the data analysis examples of the course;
4. understand and apply the addition rule and multiplication rule of probability;
5. understand the basic ideas of conditional probability including the application of the total probability theorem and Bayes' theorem;
6. understand and recognise situations appropriate for Binomial and Poisson models;
7. calculate expectations and variances for discrete and continuous random variables, understand the ideas of probability density function and the distribution function;
8. understand the change of variables formula and know how to calculate the distributions of functions of random variables;
9. understand moment generating functions;
10. 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;
11. understand the basic ideas of central limit theorem;
12. Implement in R the statistical methods described above.
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
Implement in R the statistical methods described above.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
- Upton, Graham J. G.; Cook, Ian. (1996) Understanding statistics, Oxford: Oxford University Press.
The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: 150 minutes during Summer (Main Period)
|
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
Prof Hongsheng Dai, email: hdaia@essex.ac.uk.
Dr Hongsheng Dai & Dr Yassir Rabhi
Dr Hongsheng Dai
(hdaia@essex.ac.uk), Dr Yassir Rabhi (yassir.rabhi@essex.ac.uk)
Yes
Yes
No
No external examiner information available for this module.
Available via Moodle
Of 1175 hours, 0 (0%) hours available to students:
1175 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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