# ST111 Probability A

###### Lecturer(s): Dr Martyn Parker

* Prerequisites:* MA131 Analysis I, MA132 Foundations.

* Leads to:* ST104 Statistical laboratory, ST220 Introduction to Mathematical Statistics, ST202 Stochastic Processes, MA3H2 Markov processes and percolation theory, and to numerous statistical, probabilistic, operational research and econometric courses.

* Commitment: *This module runs in Term 2.

- ST111 - 15 hours of lectures, 2 tutorial hours (week 3 and week 5)

* Aims: *To lay the foundation for all subsequent modules in probability and statistics, by introducing the key notions of mathematical probability and developing the techniques for calculating with probabilities and expectations.

**Content (part A):**

- Experiments with random outcomes: the notions of events and their probability. Operations with sets and their interpretation. The addition law and axiomatic definition of a probability space.
- Simple examples of discrete probability spaces. Methods of counting: inclusion-exclusion formula and multinomial co-efficients. Examples including the birthday problem and coupon collecting.
- Simple examples of continuous probability spaces. Points chosen uniformly at random in space.
- Independence of events. Conditional probabilities. Simpsonâ€™s paradox. Bayes theorem.
- Binomial probabilities. The law of large numbers, Poisson and Gaussian approximations and their applications.

**Books:**

- Durrett, Elementary Probability for Applications.
- Grimmett and Walsh, Probability- An Introduction.
- Grimmett and Stirzaker, One Thousand Exercises in Probability
- Sheldon Ross, A first course in Probability.

* Assessment: *10% assessed work (during term 2) and 90% written examination (in term 3).

* Examination period: *Summer

**Deadlines:**

- ST111 assignments are due on Tuesdays of weeks 4 and 6

* Feedback: *Feedback on your assignments will be given within 2 weeks of submission