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Modelling events in time
Modelling events in time

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Conclusion

Following completion of this free OpenLearn course, Modelling events in time, as well as being able to calculate probabilities associated with the Poisson processes introduced, you should also find that your statistical modelling skills are improving.

You should now 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.

This free OpenLearn course is an extract from the Open University course M343 Applications of probability [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

If you feel you are ready to move on in your study of statistics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn courses Univariate continuous distribution theory and Point estimation. They are adapted extracts from the Open University course M347 Mathematical statistics.

If you are interested in pure mathematics, you might like to try the free OpenLearn courses Number theory, Group theory, Rings and polynomials and Metric spaces and continuity.

If you are interested in applied mathematics, you might like to try the free OpenLearn courses Linear programming – the basic ideas, Introduction to the calculus of variations and Kinematics of fluids.