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Programme & Unit Catalogues

## MA10212: Probability & statistics 1B

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment: CW 25%, EX 75%
Supplementary Assessment: MA10212 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA10211
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.
Programme availability:

#### MA10212 is Compulsory on the following programmes:

Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 1
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 1
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 1
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 1
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 1
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1

#### MA10212 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 1
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 1
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.