# Modelling events in time

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Learn about probability and random processes in this free course. Understand the concepts of random events, Poisson processes, and multivariate Poisson processes. Gain the ability to calculate probabilities and simulate events using relevant tables. Enhance your knowledge of random processes and their applications.

This free course develops ideas about probability and random processes. Sections 1 and 2 introduce the fundamental ideas of random processes through a series of examples. Section 3 describes a model that is appropriate for events occurring ‘at random’ in such a way that their rate of occurrence remains constant. Section 4 derives the main results from Section 3. Section 5 introduces the multivariate Poisson process in which each event may be just one of several different types of event. Section 6 introduces the non-homogeneous Poisson process in which events occur at a rate that varies with time.

## Course learning outcomes

After studying this course, you should be able to:

Use the standard notation for random processes and identify the time domain and the state space of a random process

Decide whether a process involving Bernoulli trials is a Bernoulli process

Define the random variables X (t), X (t1, t2), Tn and Wn for a point process and use this notation when calculating probabilities associated with point processes

Calculate probabilities associated with the Poisson process, the multivariate Poisson process and the non-homogeneous Poisson process

Use relevant tables to simulate the occurrences of events in a Poisson process and in a non-homogeneous Poisson process.

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