• Probability spaces as models for chance experiments; the probability of an event as a quantity representing its long-run relative frequency
• The notion of random variable: a function on an outcome set, used to model a quantity determined by the outcome of a chance experiment.
• The expected value of a random variable, representing its expected long-run average value .
• The limit theorems: weak law of large numbers, strong law of large numbers and the central limit theorem.
• The idea of a distribution as an assignment of probability to intervals, and thence to sets that can be made from intervals by set operations; the distribution of a random variable.
• The two main kinds of distributions: discrete and absolutely continuous, and the various kinds of calculations involving them.
• The standard "brand-name" distributions and models most used in practice, including the Poisson process.
• Joint, marginal and conditional distributions.
• Distribution theory: finding the distribution of a function of one or more random variables; including the use of probability generating functions.
• Conditional probability and independence; the use of conditioning and Bayes's Theorem.

• Weekly assignments counting for 30% (Do them!)
• One midterm counting for 30 %
• One in class final counting for 40 %.