This unit introduces the basic ideas and techniques of probability, including the handling of random variables and standard probability distributions and the crucial notions of conditional probability and of independence, to equip the students with the necessary knowledge required for probability related courses in their later studies

The unit aims to introduce the basic ideas and techniques of probability, including the handing of random variables and standard probability distributions and the crucial notions of conditional probability and of independence, to equip the students with the necessary knowledge required for probability related courses in their later studies.  

On the successful completion of the course, students will be able to: 
1. describe how mathematics models randomness and model real-world situations involving randomness 
2. compute probabilities and expectations using various formulas and demonstrate why those formulas hold
3. describe standard distributions and apply them in the context of a sequence of biased coin flips, exponential waiting times, or the sum of independent random variables
4. explain and appraise statements that hold for a large class of distributions like the Central Limit Theorem, or the law of large numbers
 

The course gives a general introduction to probability theory and is a prerequisite for all future probability and statistics courses.

1. Probability space: sample space and counting principles; events and probability. 
2. Conditional probability and independence. 
3. Discrete and continuous random variables; (joint) distributions. 
4. Expectation and variance of a random variable. 
5. Classical distributions including the Binomial, Geometric, Poisson, Normal and Exponential distributions. 
6. Probability theory: The Central Limit Theorem. Law of Large Numbers. 

There are supervisions in alternate weeks which provide an opportunity for students' work to be marked and discussed and to provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour

1) S. Ross, A First Course in Probability, Macmillan.

2) D. Stirzaker, Elementary Probability, Cambridge University Press. Available electronically through the library.

3) HELM consortium, HELM Workbooks 35, 37, 38 and 39, Open Access Publication. Available electronically on the internet.