## MAS191 Introduction to Probability and Statistics 2 (NJTech)

 Semester 1, 2017/18 10 Credits Lecturer: Dr Eun-jin Kim Reading List Aims Outcomes Assessment Full Syllabus

This is the second of two modules providing an introduction to the fields of probability and statistics, which form the basis of much of applicable mathematics and operations research. The theory behind probability and statistics will be introduced, along with examples occurring in such diverse areas as medicine, finance, sport, the environment, law and so on. Some of the computational statistical work will make use of the statistics package R.

There are no prerequisites for this module.

The following modules have this module as a prerequisite:
 MAS291 Statistics Core (NJTech)

## Aims

• Introduce students to the theory of probability, including applications to practical examples;
• To develop the students' knowledge and understanding of statistics.

## Learning outcomes

• calculate standard errors and properties of sampling distributions in simple problems;
• understand the formulation of inference problems in terms of data and model parameters;
• understand the form and logical basis of significance tests, and be able to interpret such tests;
• understand the concept of a confidence interval and the relationship between confidence intervals and tests;
• understand the basis of simple inference procedures for normal expectations and binomial proportions, and be able to use the procedures in R.

32 lectures, 32 tutorials

## Assessment

One formal 2 hour written examination. All questions compulsory.

## Full syllabus

1. Introducing Statistics

2. Estimation and Uncertainty
• Estimation and the need to consider uncertainty in estimates, with examples from the media. Estimating a population mean from a sample: probabilistic modelling of random sampling from a population, and the difference between Xi and xi.
• Independent random variables. Sums of i.i.d. random variables. Chebyshev's inequality and the law of large numbers.
• The central limit theorem.
• An estimator X as a random variable.
• Bias, standard error and consistency; the expectation and variance of X.
• Estimating a proportion and a variance. Mean and variance of estimators in both cases.
• Introduction to interval estimation, confidence interval for the mean with known variance, large samples and use of the CLT.
• The case of unknown variance, the t distribution, confidence intervals for the mean with unknown variance.
• Confidence intervals for population mean, with known and unknown population variance.
• Estimating variance, the chi-square distribution, confidence intervals for the variance.
3. Hypothesis tests
• The role of statistics in medical research. The principles of hypothesis testing. A hypothesis test using the binomial distribution (e.g. the lady tasting tea). The size of a test and p-values.
• Z-test and t test (one and two sample). Implementation using R.
• The power of a test, and choosing a sample size.
4. Inference for the multinomial distribution, and analysis of contingency tables
• Inference for the multinomial, goodness of fit tests, and why the χ2 test works.
• Contingency tables, testing for independence and homogeneity, implementation in R

Type Author(s) Title Library Blackwells Amazon
B Applebaum Probability and information : an integrated approach (2nd ed) Blackwells Amazon
B Dekking, Kraaikamp, Lopuhaa and Meester A modern introduction to probability and statistics: understanding why and how Blackwells Amazon
B Grimmett and Welsh Probability : an introduction Blackwells Amazon
B Ross A first course in probability (8th ed) Blackwells Amazon
B Trosset An introduction to statistical inference and its applications with R Blackwells Amazon
C Blastland and Dilnot The tiger that isn't: seeing through a world of numbers Blackwells Amazon
C Pruim Foundations and Applications of Statistics Blackwells Amazon
C Schoenberg Introduction to probability with Texas hold'em examples Blackwells Amazon
C Silver The Signal and the Noise: The Art and Science of Prediction Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.