I have two questions:
1. Which one is determined first: (i) Random variable's values, (ii) the random experiment?
For instance this link says the following:
Suppose a variable X can take the values 1, 2, 3, or 4.
The probabilities associated with each outcome are described by the following table:
Outcome 1 2 3 4
Probability 0.1 0.3 0.4 0.2
The probability that X is equal to 2 or 3 is the sum of the two probabilities: P(X = 2 or X = 3) = P(X = 2) + P(X = 3) = 0.3 + 0.4 = 0.7. Similarly, the probability that X is greater than 1 is equal to 1 - P(X = 1) = 1 - 0.1 = 0.9, by the complement rule.
Which means, the values of Random Variables are decided first which is very unusual.
2. Can a Random Variable take random values?
For instance, can we roll a die and a random variable associated with it take on,
X = {99, 0, 100, 1, -35, 2.4} ?