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System Identification: Theory for the User, Second Edition by Lennart Ljung - Linköping University Sweden

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Appendix I. Some Concepts from Probability Theory

In this appendix we list some basic concepts and notions from probability theory that are used in the book. See a textbook like Papoulis (1965) or Chung (1979) for a proper treatment.

A random variable e describes the possible numerical outcomes of experiments whose results cannot be exactly predicted beforehand. The probability of the numerical values falling in certain ranges is then expressed by the probability density function (PDF) fe(x):

(I.1)

image

If e may assume a certain value with nonzero probability, we can think of fe containing a δ-function component of that value. A formal treatment then ...

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