I was assuming you meant range as in the statistical term (for a distribution, roughly, the maximum x for which pdf(x)≠0, minus the minimum x for which pdf(x)≠0).
Annoyingly, this is closer to the domain than it is the range, in function terminology.
I meant the image.
Are you sure? The range is a description of the possible outputs of the pdf, which means… almost nothing. Trivial counterexample if you do mean image:
Uniform distribution A between 0 and 0.5 (that is, 2 for 0..0.5, and 0 otherwise).
Uniform distribution B between 1.0 and 1.5 (that is, 2 for 1.0..1.5, and 0 otherwise).
Both of these distributions have the same image {0, 2}. And yet they are disjoint.
Honestly I wasn’t thinking much about the word “range”, and should have simply said: > Anything you draw from B could have been drawn from A.
There are many probability distributions where this is not the case. (Like the two uniform distributions A and B I give in this post.)
*****
Oh. You said you don’t know the terminology for distributions. Is it possible you’re under a misunderstanding of what a distribution is? It’s an “input” of a possible result, and an “output” of how probable that result is[1]. The output is not a result. The input is.
Oh. You said you don’t know the terminology for distributions. Is it possible you’re under a misunderstanding of what a distribution is? It’s an “input” of a possible result, and an “output” of how probable that result is.
Yup, it was that. I thought “possible values of the distribution”, and my brain output “range, like in functions”. I shall endeavor not to use a technical term when I don’t mean it or need it, because wow was this a tangent.
I was assuming you meant range as in the statistical term (for a distribution, roughly, the maximum x for which pdf(x)≠0, minus the minimum x for which pdf(x)≠0).
Annoyingly, this is closer to the domain than it is the range, in function terminology.
Are you sure? The range is a description of the possible outputs of the pdf, which means… almost nothing. Trivial counterexample if you do mean image:
Uniform distribution A between 0 and 0.5 (that is, 2 for 0..0.5, and 0 otherwise).
Uniform distribution B between 1.0 and 1.5 (that is, 2 for 1.0..1.5, and 0 otherwise).
Both of these distributions have the same image {0, 2}. And yet they are disjoint.
There are many probability distributions where this is not the case. (Like the two uniform distributions A and B I give in this post.)
*****
Oh. You said you don’t know the terminology for distributions. Is it possible you’re under a misunderstanding of what a distribution is? It’s an “input” of a possible result, and an “output” of how probable that result is[1]. The output is not a result. The input is.
...to way oversimplify, especially for continuous distributions.
Yup, it was that. I thought “possible values of the distribution”, and my brain output “range, like in functions”. I shall endeavor not to use a technical term when I don’t mean it or need it, because wow was this a tangent.