Random Variables And Stochastic Processes

Module description

The aim of this course is to introduce the fundamentals of probability theory and develop the tools needed to understand more advanced topics such as random sequences, continuous and discrete - time random processes, and filtering.

•  Review of probability and random variables. Conditional probability and independence, random variables, probability distribution and density, function of random variables, expectation, independence, conditional expectation and its properties.
• Random processes. Continuous and discrete-time random processes, correlation function and power spectrum, Gaussian and Poisson processes, continuity of random processes, differentiation and integration, stationarity and wide-sense stationarity, white noise, ergodicity.
• Systems with stochastic inputs. Transfer functions, response of linear systems to Gaussian inputs, input-output relationships, power spectral density of the output process.
• Special classes of stochastic processes. Markov Chains and their properties.

Assessment details

Written examination/s;coursework

Educational aims & objectives

The aim of this module is to introduce the fundamentals of probability theory and develop the tools needed to understand more advanced topics such as random sequences, continuous and discrete-time random processes, and filtering.

Learning outcomes

At the end of this module you should:

• Learn the fundamentals of probability and random variables, and the techniques to compute conditional probability, expectation, and its properties.

• Learn the functions of random variables such as one functions of multiple random variables and their properties.

• Learn the theory of random processes, namely, continuous and discrete-time random processes.

• Learn special classes of random processes such as Markov chains.

• Learn the systems with stochastic inputs, and the techniques to compute transfer functions, response of linear systems to Gaussian inputs, input-output relationships, and power spectral density of the output process.

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.