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Part of the reason the study of probability is so important is that it can be used to model a huge variety of real-world processes. Of course, we can't predict the outcome of a coin toss or die roll with the same model we use to predict the amount of rainfall in a given area or the outcome of a major election. These concepts are so disparate that it feels silly to even draw a connection between them -- and yet they all rely on core ideas from the same branch of mathematics.
It's clear that in order to use statistics and probability well, we need to have tools that give more information about potential outcomes than just the probability of an event as a static value. The need for more and better tools motivates the implementation of the random variable.
Part of the reason the study of probability is so important is that it can be used to model a huge variety of real-world processes. Of course, we can't predict the outcome of a coin toss or die roll with the same model we use to predict the amount of rainfall in a given area or the outcome of a major election. These concepts are so disparate that it feels silly to even draw a connection between them -- and yet they all rely on core ideas from the same branch of mathematics.
It's clear that in order to use statistics and probability well, we need to have tools that give more information about potential outcomes than just the probability of an event as a static value. The need for more and better tools motivates the implementation of the random variable.