The aim of the module Mathematics 3 is to provide the student with a working knowledge of statistical techniques so as to enable them to select and apply such techniques to the solution of engineering problems.
Programming skills: Simple and compound propositions. Truth tables. Simple logic circuits: AND, OR, NAND, NOR, EXCLUSIVE OR. Modularity in program design; use of built-in I/O and mathematical functions. User defined functions and parameter passing.
Working with data: Collecting data: tallies. Organising data: frequency tables. Graphs: frequency curves, and time series. Population and sample: inference. Summary statistics: mean, median, mode, range, standard deviation, coefficient of variation.
Probability: Definition of probability. Calculating probabilities. Permutations and combinations. The laws of probability. Reliability engineering: components in series and in parallel.
Discrete probability distributions: The binomial distribution: defectives. The Poisson distribution: defects, breakdowns.
Continuous probability distributions: The exponential distribution: failure times. The normal distribution: percentage out-of-specification. Typical non-normal patterns and their causes. Process Capability. Statistical Process Control: X-Bar charts, np charts and c charts.
Estimation: The addition of variances. The central limit theorem. Confidence intervals for means and proportions.
Testing theories: Tests of population means and proportions.
Regression and Correlation: Scatterplots. Correlation coefficient. Coefficient of determination. Regression equation. Prediction: interpolation and extrapolation.
