I have five math terminology questions about variables, realizations, variates / outcomes, and I have based my questions off my understanding of these terms from [1] 2014 MIT paper "Random Variables in a Nutshell" by AT Patera, M Yano, page 3 first paragraph:
QUESTION 1: Are "realizations", "outcomes", and “variate” strictly only applicable in the context of probability & statistics / stochastic / randomness?
QUESTION 2: Would it make sense to use these words in the context of a deterministic model?
QUESTION 3: are variates just discrete values or can they be continuous values, and if continuous then what physical example would the latter be? I base this question off my understanding of what variates are as listed in the second indented bullet below.
QUESTION 4: So would the following be true: "yielded deterministic-outcomes (e.g. discrete numerical values) from deterministic-realizations just be known as deterministic-variates"
QUESTION 5: It appears deterministic probabilities do exist [4], does anyone have any more references on that?
From [1], it is my understanding that:
- Variables are just the description of in/dependency's variation, x or X
- Realizations are the procedure of applying that variable to a specific instance/event/condition, x -> x^i
- Variate is an outcome as yielded from processing their realizations, x^i -> x^i_o elements of sample space {x^i_o}
Also, I am citing the MIT paper here and also these forums where it is being asked if variate, and covariant has meaning for deterministic systems:
[2] What is the difference between a random variate and realization of a random variable?
[4] http://philsci-archive.pitt.edu/12166/1/DeterminismIndeterminismWordPittsburghArchiveWithF.pdf