Statistics and Probability

Course Description

This module introduces the basic concepts of statistical modelling, with particular emphasis on applications in
finance and engineering. Strong emphasis is placed on using the material covered in problem-solving scenarios.
The main sections of the course are: (1) Descriptive Statistics; Mean, median, mode, range, standard deviation,
interquartile range, percentiles. (2) Graphical Methods; Pie charts, bar graphs, histograms, stem-and-leaf
plots, cumulative frequency curves, Venn diagrams. (3) Laws of Probability including; Law of total probability,
additive rule, multiplicative rule, mutually exclusive events,dependent and independent events, conditional
probability, combinations rule,permutations rule, mean and variance of functions of random variables.
(4) Discrete Distributions including; discrete random variables, E(X) and Var(X) for X discrete, binomial
distribution,poisson distribution, hypergeometric distribution. (5) Continuous Distributions; Continuous
random variables, density functions, cumulative density functions, E(X)and Var(X) for X continuous, uniform
distribution, exponential distribution, normaldistribution, Z values, standard normal distribution, Student's
t-distribution. (6) Confidence Intervals and Hypothesis Testing, Sampling distributions, biased and unbiased
estimators, significance level, CentralLimit Theorem, large sample confidence interval for a population mean,
small sampleconfidence interval for a population mean, large sample confidence interval for apopulation
proportion, sample size calculations.(7) RegressionCorrelation coefficient, residuals, simple linear
regression, correlation and causation,coefficient of determination, making predictions from the regression
equation.In addition students are required to complete a sequence of computer laboratory sessions using an
interactive package that allows them to simulate common probability problems; and use the statistical package
R to analyse data and perform regression analysis.