MA10211: Probability & statistics 1A
[Page last updated: 20 April 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Certificate (FHEQ level 4) 
Period: 

Assessment Summary:  EX 100% 
Supplementary Assessment: 

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: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021 
MA10211 is Compulsory on the following programmes:Department of Economics

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