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https://stats.stackexchange.com/questions/442265/do-all-bounded-probability-distributions-have-a-definite-mean
A bounded function satisfies f(x) < M for some M and all x in the domain. So a random variable being bounded would mean the same to me, X(w) < M for all w in the sample space. It may be common in non-mathematical domains, but I suspect most mathematicians will be a bit confused by this use of bounded before clarification.
https://math.stackexchange.com/questions/1604895/expectation-on-a-bounded-support
Expectation on a Bounded Support. Ask Question Asked 3 years, 11 months ago. Active 3 years, 11 months ago. ... probability probability-theory probability-distributions. share cite improve this question. asked Jan 8 '16 at 21:53. Fianra Fianra. 1,006 8 8 silver badges 12 12 bronze badges
https://pdfs.semanticscholar.org/20a6/3ede36953ddf4c9111936a0ffbeb9dfa5b16.pdf
that the distributions with bounded support may arise either in model or in the prior. 3.1 Uniform Distribution The uniform distribution of a random variable X ∼ U(a,b)on a compact set [a,b]has the pdf f(xa,b)=(b−a)−1 for x ∈(a,b) and moments E[X]= b−a 2 varX = (b−a)2 12. As a maximumentropydistributionunderknownsup-
https://reference.wolfram.com/language/guide/BoundedDomainDistributions.html
Bounded Domain Distributions. Bounded domain distributions naturally come up when random variables should only vary in a finite interval. Some distributions, like beta, occur in a variety of ways, including as order statistics of an underlying uniform distribution or as a …
https://www.researchgate.net/publication/303909137_Boundary_properties_of_bounded_interval_support_probability_distributions
This paper explores the properties of probability distributions as the random variables that defined those distributions approaching their bounded interval support. The models under study are:...
https://math.stackexchange.com/q/2410049?lq=1
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https://www.statlect.com/glossary/support-of-a-random-variable
Support of random vectors and random matrices. The same definition applies to random vectors. If is a random vector, its support is the set of values that it can take. The concept extends in the obvious manner also to random matrices. Synonyms. The support is sometimes also called range. More details
https://en.wikipedia.org/wiki/Infinitely_divisible_probability_distribution
Infinite divisibility (probability) In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables.
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