found in the following recommended texts: Clarke, G.M. and Cooke, D. (1998). A
Basic. Course in Statistics. 4th ed, Arnold. Daly, F., Hand, D., Jones, M., Lunn, ...
MATH 105: [Probability and] Statistics Joe Whittaker B25 Fylde College Department of Mathematics and Statistics Lancaster University April 2010 LUVLE: https://domino.lancs.ac.uk/09-10/MATH/MATH105.nsf
i
Organization The module runs for five weeks, weeks 21-25, with four lectures a week, a weekly workshop and a weekly Lab100 help session. Handouts: • Course notes • Exercises: Workshop, Quiz, Course Work. Please bring both to the lectures and workshops. The notes have gaps which are to be filled in during the lectures.
2
Your participation in the course, by taking part in experiments, contributing in lectures and workshops and responding to the questionnaire is much appreciated.
3
Timetable sun
mon
tue
wed
9-10
thu GFoxLT1
10-11
GFoxLT1
11-12
OfficeB25
WkShop4 Faraday
OfficeB25
12-1
GFoxLT1
1-2
105-QZCW due
WkShop1
2-3 3-4 4-5
WkShop2
5-6
WkShop3
11pm
fri
100-QZ due
4
Lectures: are held at 10am Tuesday, 11am Wednesday, 9am Thursday and 12 noon Friday. Workshops: will be held in Management School Lecture Theatre 7. Lists of groups are posted outside the Maths and Stats Department Office in Fylde College. • Workshops start in the first week. Labs: continue in the lab100 stream: Monday at 10; 12; 4; 5; Tuesday at 9; 11; 12; 5. Labs start in the first week, and a test in week24. Any problems, please see Julia in B4c Fylde.
5
Assessment • 20% Course Work (10% quiz + 10% written), • 30% end-of-term test (Friday week 25), • 50% final exam. Deadlines Online quiz questions (labelled QZ) should be completed by 2pm on the following Wednesday. Homework questions (labelled CW) should be handed in by 2pm on the following Wednesday in your tutor’s pigeonhole. • Solutions are posted on the course webpage.
6
Labs The Lab100 course is running in parallel with math105. Weekly help sessions are available. You are expected to have downloaded R on to your computer. The first lectures are on R, and are examinable in math105.
7
Preliminaries The math105 course continues on from math104, very directly. • Firstly you have met R in the lab100 work associated with math104. Both math104 and math105 require R and the first Chapter here goes over a tutorial introduction to some of the basic concepts of the language.
8
• Secondly, the extension of probability from discrete random variables, discussed in math104, to continuous random variables is discussed here. Both the discrete and the continous cases are needed for statistics. The mathematical prerequisites for the analysis of continuous random variables is the integral calculus of math101.
9
• The third part of the course introduces the statistical methods which are required for tackling a range of applied problems. The focus is on strategies for data modelling rather than mathematical theory. However, there is some theory, and we aim to introduce basic concepts as it will be taught fully in later statistics courses. Data examples are used throughout the course, to illustrate the techniques that the course aims to teach you. The course data sets are on the LUVLE course web. 10
At the end of this course, you should be able to: • understand the basic concepts and objects of the R language, including some elements of programming; • define the basic concepts of continuous random variables, the probability density function and the cumulative distribution function; • have familiarity with some standard continuous random variables, such as the Uniform, Exponential and Normal; be aware of their parameters and how these relate to expectations. 11
• use R to make computations and plots of the cdf, and of quantiles derived from it; • use R to simulate from standard distributions; • use graphical tools such as histograms, scatterplots, empirical distribution function and the boxplot; • calculate and understand numerical summary statistics such as mean, median, variance, quantiles and the correlation coefficient; • discuss a range of modelling assumptions that can play a part in statistical analysis.
12
Background reading Although the lectures and these accompanying notes are self-contained, further details can be found in the following recommended texts: Clarke, G.M. and Cooke, D. (1998). A Basic Course in Statistics. 4th ed, Arnold. Daly, F., Hand, D., Jones, M., Lunn, A. and McConway, K. (1995). Elements of Statistics. Addison Wesley. Lindsey, J. (1995). Introductory Statistics: A Modelling Approach. Oxford Science Publications.
13
