STU12501 – Introduction to Statistics I (Probability)

Module CodeSTU12501
Module NameIntroduction to Statistics I (Probability)
ECTS Weighting[1]5 ECTS
Semester taughtSemester 1
Module Coordinator/s  Fergal Shevlin

Module Learning Outcomes

  1. Understand the elementary concepts of probability models.
  2. Apply various probability models to practical problems in a range of disciplines.
  3. Distinguish between discrete and continuous random variables.
  4. Appreciate the elementary properties of random variables.

Module Content

  • Sample Space and Probability: Sets; Probabilistic Models; Conditional Probability; Total Probability.
  • Theorem and Bayes’ Rule; Independence; Counting.
  • Discrete Random Variables: Probability Mass Functions; Functions of Random Variables.
  • Expectation, Mean, and Variance; Joint PMFs of Multiple Random Variables; Conditioning.
  • Independence.
  • General Random Variables: Continuous Random Variables and PDFs; Cumulative Distribution.
  • Functions; Normal Random Variables; Joint PDFs of Multiple Random Variables; Conditioning.
  • Continuous Bayes’ Rule.

Teaching and learning Methods

Lectures, homework, tutorials.

Assessment Details

Assessment ComponentBrief DescriptionLearning Outcomes Addressed% of totalWeek setWeek Due
ExaminationTake-at-home examination, time-limited.LO1,2,3,4.100

Reassessment Details

Take-at-home examination, time-limited, 100%.

Contact Hours and Indicative Student Workload

Contact Hours (scheduled hours per student over full module), broken down by:33 hours
Lectures (11 weeks x 2 hours.)22 hours
Laboratory0 hours
Tutorials (11 weeks x 1 hour.)11 hours
Other0 hours
Independent study (outside scheduled contact hours), broken down by:92 hours
Suggested lecture preparation (11 weeks x 3 hours.)33 hours
Suggested homework problem-solving (11 weeks x 3 hours.)33 hours
Exam preparation (2 weeks x 13 hours.)26 hours
Total Hours125 hours

Recommended Reading List

Extensive on-line course material associated with “Introduction to Probability”, 2nd Edition, Bertsekas and Tsitsiklis, Athena Scientific.

Module Pre-requisites

None.

Module Co-requisites

None.

Module Website

See TCD Blackboard.