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MA10212: Probability & statistics 1B

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Certificate (FHEQ level 4)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework 1 (CW 6%)
  • Coursework 2 (CW 6%)
  • Coursework 3 (CW 6%)
  • Coursework 4 (CW 7%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA10211
Further information on descriptions Description: Aims:
To introduce probability theory for continuous random variables. To introduce statistical modelling and parameter estimation and to discuss the role of statistical computing.

Learning Outcomes:
After taking this unit the students should be able to:
* Solve a variety of problems and compute common quantities relating to continuous random variables.
* Formulate, fit and assess some statistical models.
* Use the R statistical package for simulation and data exploration.

Skills:
Numeracy T/F A
Problem Solving T/F A
Data Analysis T/F A
Information Technology T/F A
Written and Spoken Communication F (in tutorials).

Content:
Definition of continuous random variables (RVs), cumulative distribution functions (CDFs) and probability density functions (PDFs).
Some common continuous distributions including uniform, exponential and normal.
Transformations of RVs. Discussion of the role of simulation in statistics. Use of uniform random variables to simulate (and illustrate) some common families of discrete and continuous RVs.
Results for continuous RVs analogous to the discrete RV case, including mean, variance, standard deviation, properties of expectation, joint PDFs (including dependent and independent examples), independence (including joint distribution as a product of marginals), covariance, correlation.
The distribution of a sum of continuous RVs, including normal and exponential examples. Statement of the central limit theorem (CLT).
Introduction to model fitting; exploratory data analysis (EDA) and model formulation. Parameter estimation via method of moments and (simple cases of) maximum likelihood.
Sampling distributions, particularly of sample means. Point estimates and estimators. Estimators as random variables. Bias and precision of estimators.
Graphical assessment of goodness of fit.
Further information on programme availabilityProgramme availability:

MA10212 is Compulsory on the following programmes:

Department of Economics
  • UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
  • UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
  • UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
  • UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 1)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 1)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)

Notes: