This course introduces students to key concepts from probability theory and provides an introduction to survey sampling with a focus on the underpinning probabilistic mechanisms.

The course mostly consists of asynchronous teaching material.

Statistics 2R: Probability

Statistics 2X: Probability II

Probability (Level M)

Probability and Stochastic Models (ODL)

Sampling Fundamentals (ODL)

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Assessment will typically be made up of a class test worth 75% and online quizzes worth a total of 25%.

Additionally, students must pass 4 maths assessments. Students are required to obtain at least 75% of the available marks in each maths assessment to pass. Students must pass all four assessments. Failing to pass any of the 4 maths assessments will result in a cap being placed on the course grade.

1. Students who pass the 4 maths assessments by the end of May will have their probability course grade returned as per the summative assessment detailed above.

2. Students who fail to pass all 4 maths assessments by the end of May will be returned a capped grade of E1 for their probability course.

3. Students who fail to pass any of the four maths assessments will be offered an opportunity to reattempt these during the August reassessment period.

4. Students who fail to pass any of the four maths assessments after the reassessment stage will be returned a   capped grade of E1

The course aims to introduce students to probability theory with a focus on understanding and being able to apply concepts, rather than deriving these concepts in a mathematically rigorous manner. Students will be introduced to key concepts in probability theory, univariate and multivariate random variables developing and moments. The course aims to prepare students to solve real-life problems using stochastic models.
Using the concepts from probability covered in the first part of the course, the course introduces students to sampling from a finite population. The course aims to equip students with an understanding of key concepts in sampling such as the difference between sampling with and without replacement, stratification and nonresponse.

By the end of this course students will be able to:

■ use probability mass functions, probability density functions and cumulative distribution functions in one or more dimensions to compute probabilities and percentiles in particular cases;

■ compute moments in one or more dimensions (including the vector of expected values and the variance-covariance matrix) for given distributions and interpret them;

■ recognise some of the standard discrete and continuous probability distributions in a context, and use them to obtain probabilities, percentiles and moments;

■ use the joint distribution of a random vector to derive marginal or conditional distributions of one or more of the component variables;

■ determine whether two or more random vectors are independent;

■ explain and apply key concepts in large sample theory;

■ state and use properties of the multinomial and Multivariate Normal (MVN) distribution;

■ explain the difference between different strategies for sampling in a probabilistic context and discuss advantages and disadvantages of these strategies in a context;

■ estimate parameters and their uncertainty in a finite population; and

■ integrate their knowledge of topics in the course to solve realistic problems.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment. Students must also pass the maths core skills component.