Random variable

A random variable is simply a mapping between all possible experimental outcomes and a numerical value. For example, in coin tossing all experimental outcomes are $$H, T$$ and the numerical values are generally $$0, 1$$; the random variable is nothing but a function that does this mapping. The name random variable is somewhat disappointing as there is nothing random about this function, it just maps $$H$$ to $$0$$ and $$T$$ to 1, pretty deterministicly. What is random is the outcome of the experiment; we don't know if we'll have $$H$$ or $$T$$.