Biagini, F., & Campanino, M. (2016). Elements of Probability and Statistics, p. 3-12
Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques, p. 15-21
The rendition in Biagini is slightly more coherent and link between logical operations and random variables are more evident. The terminology is limiting though. It only concerns itself with random variables that have real numbers or integers as its set of possible outcomes.
The rendition in Koller & Friedman is more relaxed. Random variable can have a character function, which can map anything to anything measurable really, however it's random variables job to assign a value to the outcome of character function.
These two references are diametrically oppose to each other in how they introduce the subject. Biagini starts from random numbers then derives events and expectations and finally probability of events from random numbers' properties. Koller starts of with the probability distribution, enumerates types of probability distribution and their properties, then settles on random variables.
I am more inclined towards Biagini as it opens up more smoothly to discrete and continuous variables later on. We can always use graph_data attribute to store non numeric outcomes and assign them to their numeric representation in the set of possible outcomes of the random variable via some function. But it is up for discussion
There are two candidates:
The rendition in Biagini is slightly more coherent and link between logical operations and random variables are more evident. The terminology is limiting though. It only concerns itself with random variables that have real numbers or integers as its set of possible outcomes.
The rendition in Koller & Friedman is more relaxed. Random variable can have a character function, which can map anything to anything measurable really, however it's random variables job to assign a value to the outcome of character function.
These two references are diametrically oppose to each other in how they introduce the subject. Biagini starts from random numbers then derives events and expectations and finally probability of events from random numbers' properties. Koller starts of with the probability distribution, enumerates types of probability distribution and their properties, then settles on random variables.
I am more inclined towards Biagini as it opens up more smoothly to discrete and continuous variables later on. We can always use graph_data attribute to store non numeric outcomes and assign them to their numeric representation in the set of possible outcomes of the random variable via some function. But it is up for discussion