The random variable, or how to crunch some numbers
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Sometimes the raw information gathered is qualitative in nature. Sometimes, too, quantitative information needs to be transformed. This is where the notion of a random variable comes in, which can be seen either as a numerical association with qualitative observations, or as a transformation of numerical observations.
Let Ω denote the set of all the categories or values that can be associated with a random phenomenon: to each element v of Ω, we assign a numerical value x (ω). This association can involve a finite number of possible values. In that case we speak of a discrete random variable. If all the values of an interval, bounded or not, of the real line can be put in correspondence with the raw observations, we obtain a continuous random variable.
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Density function and distribution function
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