CODE 
SOR1201 

TITLE 
Probability, Sampling and Estimation 

LEVEL 
01  Year 1 in Modular Undergraduate Course 

ECTS CREDITS 
4 

DEPARTMENT 
Statistics and Operations Research 

DESCRIPTION 
 Elementary Probability  Sample space, events and probability of events  Mutually exclusive and independent events  Combinatorial Probability  Bayes’ Theorem  Random Variables  Discrete and continuous random variables  Expectation and Variance  Discrete Probability Distributions  Binomial Distribution  Poisson Distribution  Geometric Distribution  Continuous Probability Distributions  Exponential Distribution  Normal Distribution  Basic use of SPSS  Sampling Techniques  Sampling Distributions  Inference through confidence intervals  Inference through hypothesis testing  Type I and Type II Errors  Tests on means, proportions and difference of means of large and small samples  One Sample Ttest  Paired Samples Ttest  Independent Samples Ttest  Chi Square test  Pearson Correlation  OneWay ANOVA
Studyunit Aims:
 Discriminate between two selection methods (with and without replacement) and familiarize with different types of enumeration (multiplication rule, combinations and permutations).  Describe the properties of probability and use probability theory to solve problems for mutually exclusive events, independent events and conditional events.  Discriminate between discrete and continuous random variables and compute their expected value and variance.  Discriminate between different discrete distributions (Binomial, Poisson and Geometric) and use these distributions to calculate the probabilities of discretetype of random variables.  Familiarize with different sampling techniques (Random, Systematic, Stratified and Cluster sampling).  Derive sampling distributions for sample means, proportions, difference of means and difference of proportions.  Determine sample size and address uncertainty by providing margin of errors.  Carry out statistical inference using confidence intervals and hypothesis testing.  Apply statistical tests (OneSample, Independent Samples, Paired Samples ttests and OneWay ANOVA test) to compare means between population parameters.  Apply statistical test (Pearson correlation test) to assess the relationship between two variables having a metric scale.  Apply statistical test (Chi Squared test) to assess the association between two categorical variables.
Learning Outcomes:
1. Knowledge & Understanding:
By the end of the studyunit the student will be able to:  Understand the fundamental concepts of enumerative combinatorics (combinations and permutations) and analytic combinatorics (probability theory);  Familiarize with the concepts of expectation and variation and use these statistical tools to estimate the mean and variance of discrete and continuous random variables;  Discriminate between different types of discrete and continuous distributions and use these distributions to compute the probabilities of events;  Understand the difference between sample statistics and population parameters;  Familiarize with different sampling distributions of sample means, proportions, difference of means and difference of proportions;  Familiarize with different ways of making statistical inference, mainly by computing confidence intervals and conducting hypothesis tests.
2. Skills:
By the end of the studyunit the student will be able to:  Solve real life problems related to combinatorics and probability;  Identify the appropriate distribution of specific discrete and continuous variables and use the properties of these distributions to solve probability problems;  Use computer software, particularly EXCEL and R, to compute the probabilities of events for specific distributions, including the Binomial, Poisson, Geometric, Exponential and Normal distribution;  Conduct statistical inference about a population parameter using sample statistics;  Compute confidence interval for population means, proportions, difference of means, difference of proportions, variances and variance ratios;  Use computer software, particularly SPSS and EXCEL, to conduct statistical test including the One Sample ttest, Independent Samples ttest, Paired Samples ttest, Chi Squared test, Pearson Correlation test and the OneWay ANOVA test.
Main Text/s and any supplementary readings:
 Freund, J. E. and Miller, I. (1977) Probability and Statistics for Engineers, Prentice Hall Inc.  Callender, J.T. and Jackson, R. (1996) Exploring Probability and Statistics with Spreadsheets – Prentice Hall Inc.  Montgomery, D. and Runger, G. (1999) Applied Statistics and Probability for Engineers – Second Edition, Wiley.  Ross, S. M. (1999) Introduction to Probability & Statistics for Engineers – Second Edition, Academic.  Johnson, R. A. (1994) Miller and Freund’s Probability & Statistics for Engineers – Fifth Edition, Prentice Hall Inc. Int. Paperback Editions.  Wilson, C. (1972) Applied Statistics for Engineers – First Edition, Applied Science Publishers.  Ross, Sheldon M. (2005) Introductory Statistics – Second Edition, Academic Press.


ADDITIONAL NOTES 
Prerequisite Qualification: Pure or Applied Mathematics at the level requested for entry to Engineering and Technology courses.
Statistics & O.R. studyunits for students with 'A' Level Mathematics.
This studyunit is not for students taking Statistics & O.R. as one of the principal subject area. 

STUDYUNIT TYPE 
Lecture 

METHOD OF ASSESSMENT 
Assessment Component/s 
Resit Availability 
Weighting 
Computerbased Examination
(1 Hour and 30 Minutes)

Yes 
50% 
Computerbased Examination
(1 Hour and 30 Minutes)

Yes 
50% 


LECTURER/S 
Liberato Camilleri


The University makes every effort to ensure that the published Courses Plans, Programmes of Study and StudyUnit information are complete and uptodate at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the studyunit description above applies to the academic year 2017/8, if studyunit is available during this academic year, and may be subject to change in subsequent years.

20 October 2017
http://www.um.edu.mt/science/studyunit

