F18XS - Mathematics 4

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Aims

Study and explore the laws of random phenomena in the objective world

Syllabus

1.1 Introduction to Probability Theory, covering Random occurrence and probability, Random variable and distribution function, N-dimensional random variable and joint probability distribution, Numerical characteristics of random variables, Bernoulli’s law of large numbers and central limit theorem

2.1 Basic concepts of mathematical statistics, Parameter estimation, Hypothesis testing

Learning outcomes

By the end of the course, students should be able to do the following:

explain fundamental probability concepts including axioms, conditional probability, and Bayes' theorem
calculate distributions and properties of random variables using common probability distributions
Apply the Central Limit Theorem (CLT) to approximate probabilities and analyse sampling distributions
conduct hypothesis tests to make inferences about population parameters
construct confidence intervals to make inferences about population parameters

Further details

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SCQF Level: 8

Credits: 15