Overview of the MATH1715 course at the University of Leeds a summary “Probability is basically common sense reduced to calculation; it allows us to appreciate exactly what the rational mind feels through a certain instinct. So says Laplace. In the modern technological world, it is even more important to understand probability arguments. Probability is discussed and key ideas of random variables, including the concepts of prior and posterior distributions. two goals After completing this module students should be able to: (a) Exploratory data analysis using statistical packages (b) state and use the basic rules of probability (c) understand discrete and continuous probability models (d) understand the concepts of prior and posterior probabilities Three Syllabus 1. Exploratory Data Analysis: Numerical and Graphical Summaries. 2. Introduction to the axioms of probability and the rules of probability. 3. Joint and conditional probability, independence, and Bayesian formulas. 4. Discrete random variable, Bernoulli test, binomial distribution. 5. Continuous random variables. Uniform, exponential, and normal distributions. 6. Data and parametric models. 7. Expectation and variance. 8. Possibility. 9. Prior and posterior distributions.