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Programme & Unit Catalogues

## MA10211: Probability & statistics 1A

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: MA10211 Mandatory extra work (where allowed by programme regulations)
Requisites: You must have A level Mathematics Grade A, or equivalent in order to take this unit.
Description: Aims:
To provide a solid foundation in discrete probability theory that will facilitate further study in probability and statistics.

Learning Outcomes:
After taking this unit the students should be able to:
* Apply the axioms and basic laws of probability using proper notation and rigorous arguments.
* Solve a variety of problems with probability, including the use of combinations, permutations and standard discrete probability distributions.
* Perform common expectation calculations.
* Calculate marginal and conditional distributions of discrete random variables from joint distributions.
* Calculate and make use of some simple probability generating functions.

Skills:
Numeracy T/F A
Problem Solving T/F A
Data Analysis TF/A
Written and Spoken Communication F (in tutorials)

Content:
Sample space, events as sets, unions and intersections.
Axioms and laws of probability. Inclusion-exclusion principle.
Equally likely events. Combinations and permutations.
Sampling methods: with or without ordering and replacement.
Conditional probability. Partition Theorem. Bayes' Theorem. Simpson's paradox.
Independence of events. Bernoulli trials.
Discrete random variables (RVs). Probability mass function (PMF).
Bernoulli, Geometric, Binomial, multinomial and Poisson Distributions.
Poisson limit of Binomial distribution. Stirling's formula.
Hypergeometric Distribution. Negative binomial distribution.
Joint and marginal distributions.
Independence of RVs. Distribution of a sum of discrete RVs.
Expectation of discrete RVs. Means. Properties of expectation.
Expectation of a function. Indicator RVs. Expectation of product of independent RVs. Moments. Variance and properties. Standard deviation. Covariance, correlation.
Variance of a sum, including independent case.
Markov's inequality. Chebychev's inequality. Cauchy-Schwartz inequality
Conditional distributions. Conditional expectation.
Probability generating functions (PGFs) and basic properties.
Programme availability:

#### MA10211 is Compulsory on the following programmes:

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
• USMA-AFB05 : BSc(Hons) Statistics (Year 1)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 1)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.