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Definition

Mathematically, a random variable is defined as a measurable function from a probability space to some measurable space. More detailed, a random variable is a function

$\displaystyle X:\Omega \to \mathbb{R}$

with $ \Omega$ = the set of observable events and $ \mathbb{R}$ being the set associated to the measurable space. Observable events in the context of software models can be for example response times of a service call, the execution of a branch, the number of loop iterations, or abstractions of the parameters, like their actual size or type. Note, that often a random variable has a certain unit (like seconds or number of bytes, etc.). It is important for the user of prediction methods to keep the units in the calculations and in the output to increase the understandability of the results.

A random variable $ X$ is usually characterised by stochastical means. Besides statistical characterisations, like mean or standard deviation, a more detailed description is the probability distribution. A probability distribution yields the probability of $ X$ taking a certain value. It is often abbreviated by $ P(X=t)$. For discrete random variables, it can be specified by a probability mass function (PMF). For continuous variables, a probability density function (PDF) is needed. However, for non-standard PDFs it is hard to find a closed form (a formula describing the PDF). Because of this and for reasons of computational complexity, we use discretisized PDFs in our model.

For the event spaces $ \Omega$ we support include integer values $ \mathbb{N}$, real values $ \mathbb{R}$, boolean values and enumeration types (like "sorted" and "unsorted") for discrete variables and $ \mathbb{R}$ for continuous variables.


next up previous contents index
Next: PDF discretisation Up: Random Variables Previous: Overview   Contents   Index
Snowball 2007-03-16