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As introduced above we support the use of discrete as well as continuous variables. However, in such a case special care has to be taken when constructing expressions. Three times of a discrete variable can not be determined in the same way as three times a continuous variable. The reason for this is that continuous variables are also scaled continuously. To give an example, consider the continuous variable X which is uniformly distributed in a range between 5 and 10 seconds. If the variable is now multiplied by three, possible values of the resulting random variable can be in the interval between 15 and 30 seconds. The resulting distribution is again uniformly distributed having a density function which is one-third of the original density function.
An analogous example for a discrete random variable follows. Consider a discrete random variable taking the value 5 in 30% of all cases, 7 in 20% of all cases and 10 in the remaining 50%. If this variable is multiplied by 3, the result is a variable taking the value 15 in 30%, 21 in 20% and 30 in 50% of all cases. The probabilities of the single events stay the same only the actual outcome changes.
The depicted difference is especially important in the case of discretisized PDFs. Any mathematical operation in which such a variable is involved has to treat the discretisized PDF as a 'real' PDF in order to avoid calculation mistakes.
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Snowball
2007-03-16