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Session 4 - Introduction to Statistics

Session Objectives:

At the end of this session you will

  • understand basic concepts in probabilty theory such as random variables, conditional probabilities and independence;
  • be familiar with standard discrete and continuous distributions;
  • be able to compute and manipulate expectations, variances and covariances;
  • have acquired knowledge about simple limit theorems;
  • be able to perform simple maximum likelihood estimation and hypothesis testing;
  • be able to do simple probabilistic computations and graphical displays in the statistical package called R.

In this session, please work through the lecture notes provided. The notes contain exercises with which you can practise what you have learnt and also prepare yourself for the assessment. Solutions for the exercises are at the end of the notes, but please have a go at the exercises before checking the solutions. The notes also contain a section on a statistical package called R. This software will be used in the module CY904 Monte Carlo methods but is not part of the assessment.

Click here for the lecture notes.


  • S. Ross: A first course in probability, 7th edition, Pearson, 2006.
  • G. Casella and R.L. Berger: Statistical inference, 2nd edition, Duxbury Press, 2002.

Session Assessment:

This part of the module is assessed by an online test. There are two tests available for this Session:

  1. A practice test called Walsh CY900 S4 MOCK TEST 2005
  2. The REAL test called Walsh CY900 S4 REAL TEST 2005

To take this test, you will need the following question sheet: Questions

You can take the mock test an unlimited number of times. However, you have at most 3 attempts to pass the real test.

The pass rate is 70%.

To take the test, follow the link below, and then log in with the userid and password that I will assign to you on Day 1 of the module.

You should try to pass this test ASAP, but the deadline for completion of ALL tests is September 30th.

Online tests - Perception