## MA10211: Probability & statistics 1A

[Page last updated: 20 April 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Aims: To provide a solid foundation in 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 probability distributions.
* Perform common expectation calculations.
* Calculate marginal and conditional distributions of discrete random variables from joint distributions.
* Calculate and explore the behaviour of sums of independent random variables.

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. Equally likely events. Sampling methods: with or without ordering and replacement.
Conditional probability. Partition Theorem. Bayes' Theorem.�
Independence of events. Bernoulli trials.
Discrete random variables (RVs). Probability mass function (PMF).
Bernoulli, Geometric, Binomial and Poisson Distributions.
Joint and marginal discrete distributions.
Definition of continuous random variables (RVs), cumulative distribution functions (CDFs) and probability density functions (PDFs).
Some common continuous distributions including uniform, exponential and normal.
Independence of RVs (including joint distribution as a product of marginals),
Expectation of RVs. Properties of expectation.
Expectation of product of independent RVs. Variance and properties. Standard deviation. Moments Covariance, correlation.
Sums of independent random variables.
Key application: Random walks.
Statement of the law of large numbers.

Programme availability:

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

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (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-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-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial 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)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change 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.Find out more about these and other important University terms and conditions here.