619-202 Statistics

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Objectives:

Students completing this course should:

Comprehend:

• the fundamental concepts of probability and statistics;

• the theory underlying statistical inference;

• the basic principles of experimental design.

Have developed the skills:

• to use probability models and distribution theory in applications to standard situations;

• to carry out standard statistical analyses.

Appreciate:

• the breadth of application of probability and statistics;

• the importance of the underlying mathematical theory of statistics;

• the application of computer software in probability calculations, simulation and statistical analysis.

Content:

Random variables and descriptions of their probability distributions with particular emphasis on continuous distributions; probability mass function, probability density function; cumulative distribution function and quantiles; expectation; standard continuous probability distributions including uniform, exponential, gamma and normal distributions and some of their applications. Mean, variance and other moments; moment generating functions. Transformations: distribution of g(X) and approximations for the mean and variance of g(X).

Bivariate random variables and descriptions of their probability distributions; bivariate normal distribution; covariance and correlation; independence of random variables; distribution of g(X,Y), where X and Y are independent, including sums, products and ratios; conditional distributions and use of conditional means and variances to evaluate means and variances.

Random sampling and properties of random samples; review of descriptive statistics; distributions of statistics, in particular sample mean and sample frequencies; distribution of sample mean and sample variance for sampling from a normal distribution.

Estimation of parameters of probability distributions. Point estimation and interval estimation. Methods of estimation: method of moments; maximum likelihood estimation. Confidence intervals and prediction intervals. Likelihood intervals. Introduction to Bayesian methods. Hypothesis testing; likelihood ratio tests.

The theory and applications of the general linear model with particular reference to regression problems including multiple and polynomial regression, the analysis of one-way and two-way classifications and the analysis of standard statistical experiments; the basic principles of experimental design.

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