Re:Do not confuse a random variable with its distribution
by eru on Tuesday June 25, 2024 @11:54PM
(#40796224)
> Random variables are neither random nor variables! They are functions that map a space of random events onto the real number line![0]
They are functions that map from the space of random events to whatever other space you want. Why restrict yourself to the real number line?
Eg the 'moral character of the next stranger I encounter' is a random variable that maps from some abstract space of random events (we often used the Greek letter Omega for that) onto some space of moral characters.
And if you want to restrict yourself to numbers, why restrict yourself to reals? Why not complex numbers or p-adic numbers or numbers in F_5 or numbers in [0, 1] or 'natural numbers expect 17'?
EDIT: looks like you are right in English! See https://news.ycombinator.com/item?id=40796146 and my reply there.
Re:Do not confuse a random variable with its distribution
by kqr on Wednesday June 26, 2024 @12:56AM
(#40796513)
Now you're doing the thing the headline asks you not to do! The distribution is a function mapping events to the real number line.
Edit: I misread. I agree with you. Sorry!
Re:Do not confuse a random variable with its distribution
by throwaway199956 on Wednesday June 26, 2024 @12:57AM
(#40796521)
For continuous probability distributions, the pmf(x) has value of 0 for all real x, as per the text books.
When you're asking P(Heads) of a coin, its short hand for "P(event=heads) for all possible events that can happen when flipping a coin". You notice that in this idealized world the event is always two things (heads or tails), and never null, side, cow because we have defined that the P(event=cow) = 0.
Probability functions are at the end of the day models that we can use to analyze real world non-deterministic phenomena with the rigor of mathematics.
[0] - with credit to Prof Gubner https://directory.engr.wisc.edu/ece/Faculty/Gubner_John/