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MA10211: Probability & statistics 1A

Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 1
Assessment: 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 Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 1
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 1
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 1
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 1
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 1
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 1
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 1

MA10211 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 1
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 1
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.