Probability Theory I

University of Reading

Course Description

  • Course Name

    Probability Theory I

  • Host University

    University of Reading

  • Location

    Reading, England

  • Area of Study

    Mathematics, Statistics

  • Language Level

    Taught In English

  • Prerequisites

    Pre-requisites: ST1PD Probability and Distributions MA1FM Foundations of Mathematics
    Non-modular pre-requisites:

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    5
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4
  • Overview

    Summary module description:
    The module rigorously introduces basic concepts of probability from a mathematical perspective. It aims to equip the students with a basic knowledge in probability which will reveal the interplay between probability theory and fundamental areas of mathematics such as analysis and algebra, will allow students to formulate general real or abstract problems in a probabilistic model and will unravel the fundamentals which statistical methods are built on. In more detail the module will be developed around the concepts of probability distributions, random variables, independence, sums of random variables, limit laws and their application (Central Limit Theorem and laws of large numbers), and structures that depend on the present to study the future evolution of stochastic phenomena (Markov chains).

    Aims:
    This module aims to introduce students to some of the fundamental concepts and results of probability. It covers random variables together with probability distributions as the fundamental objects of probability theory, the concept of dependence/independence, which lead then to fundamental asymptotic results as well as a first introduction of stochastic processes such as Markov chains.

    Assessable learning outcomes:
    By the end of the module the students are expected to be able to:
    - Identify and demonstrate understanding of the main concepts and definitions in probability theory
    - Without the help of notes to state all and prove some of the main results
    - Identify and formulate problems in terms of probability and solve them to build up a simple stochastic model
    - Use the main results to do various approximations.

    Additional outcomes:
    At the end of the module students will have some insight in the interrelation between analysis, linear algebra and probability and their relevance for applications.

    Outline content:
    Random variables with uniform distribution, continuous and discrete, distributions with densities and weights, expectation of random variables, the concept of independence, sums of independent random variables, concepts of convergence of random variables, dependent random variables and conditional distributions, random transitions and Markov chains.

    Brief description of teaching and learning methods:
    Lectures, supported by problem sheets and lecture-based tutorials.

    Summative Assessment Methods:
    Written exam 75%
    Set exercise 25%

    Other information on summative assessment:
    Two assignments and one examination

    Formative assessment methods:
    Problem sheets.

    Penalties for late submission:
    The Module Convener will apply the following penalties for work submitted late, in accordance with the University policy.
    where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
    where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

    The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
    You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

    Length of examination:
    2 hours

    Requirements for a pass:
    A mark of 40% overall

Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.