# Study-Unit Description

﻿
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 T-test
- Paired Samples T-test
- Independent Samples T-test
- Chi Square test
- Pearson Correlation
- One-Way ANOVA

Study-unit 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 discrete-type 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 (One-Sample, Independent Samples, Paired Samples t-tests and One-Way 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 study-unit 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 study-unit 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 t-test, Independent Samples t-test, Paired Samples t-test, Chi Squared test, Pearson Correlation test and the One-Way 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 Pre-requisite Qualification: Pure or Applied Mathematics at the level requested for entry to Engineering and Technology courses.

Statistics & O.R. study-units for students with 'A' Level Mathematics.

SOR1201 may be taken by Physics students with an intermediate level Pure Maths only if they have completed the study-unit PHY1125 or if they will be following PHY1125 concurrently.

This study-unit is not for students taking Statistics & O.R. as one of the principal subject area.

STUDY-UNIT TYPE Lecture

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Open Book Computer-based Examination (1 Hour and 30 Minutes) SEM1 Yes 50% Open Book Computer-based Examination (1 Hour and 30 Minutes) SEM2 Yes 50%

LECTURER/S Louisa Testa
David Paul Suda

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date 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 description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit