Department of Mathematical Sciences, Unit Catalogue 2011/12
|Level:||Certificate (FHEQ level 4)|
|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.|
To provide a solid foundation in discrete probability theory that will facilitate further study in probability and statistics.
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.
Numeracy T/F A
Problem Solving T/F A
Data Analysis TF/A
Written and Spoken Communication F (in tutorials)
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.
MA10211 is Compulsory on the following programmes:Department of Mathematical Sciences
MA10211 is Optional on the following programmes:Programmes in Natural Sciences