I have a simple question: categorical random variables formally exist?
Following the Wikipedia's definition of a random variable (and also in other sites), it seems that random variables are mapping functions that map real-word events always to numbers.
Hence, if you are modelling categorical events in the real world, like flip a coin or pull colored balls out of a bag, then you use discrete numerical random variables and their associated probability distributions (binomial or multinomial), and if you are modelling continuous real world events then you use continuous numerical random variables.
Is that correct? Of course that categorical variables exist, but are there also categorical random variables? Or random variables are always numerical?
Thanks
