Department of Mathematical Sciences, Unit Catalogue 2010/11 |
MA10212: Probability & statistics 1B |
 Credits:
| 6 |
| Level:
| Certificate |
| Period: | This unit is available in... |
| 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. |