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https://www.statlect.com/glossary/support-of-a-random-variable
Support of a discrete variable For discrete random variables, it is the set of all the realizations that have a strictly positive probability of being observed. Example If a discrete random variable has probability mass function its support, denoted by, is Support of a continuous variable
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.
http://thirdorderscientist.org/homoclinic-orbit/2013/10/24/kernel-density-estimation-for-random-variables-with-bounded-support-mdash-the-transformation-trick
Kernel Density Estimation for Random Variables with Bounded Support — The Transformation Trick Something that has bothered me since I started using kernel density estimators in place of histograms 1 is that I didn't see a natural way to deal with random variables with finite support.
https://mathoverflow.net/questions/3525/when-are-probability-distributions-completely-determined-by-their-moments
When are probability distributions completely determined by their moments? Ask Question Asked 10 years, ... One sufficient condition is that if the moment generating function of a random variable has positive radius of convergence, then that random variable is determined by its moments. ... If X and Y have bounded support, the CDFs of X and Y ...
https://www.physicsforums.com/threads/show-that-if-x-is-a-bounded-random-variable-then-e-x-exists.570584/
Jan 25, 2012 · Homework Statement Show that if X is a bounded random variable, then E(X) exists. Homework Equations The Attempt at a Solution I am having trouble of finding out where to begin this proof. This is what I got so far: Suppose X is bounded. Then there exists two numbers a …
https://en.wikipedia.org/wiki/List_of_probability_distributions
Many probability distributions that are important in theory or applications have been given specific names. ... The generalized Pareto distribution has a support which is either bounded below only, ... For any set of independent random variables the probability density function of their joint distribution is the product of their individual ...
https://ocw.mit.edu/courses/mathematics/18-s997-high-dimensional-statistics-spring-2015/lecture-notes/MIT18_S997S15_Chapter1.pdf
Chapter. 1 . Sub-Gaussian Random Variables . 1.1 GAUSSIAN TAILS AND MGF . Recall that a random variable X ∈ IR has Gaussian distribution iff it has a density p with respect to the Lebesgue measure on IR given by . 1 (x −µ) 2 . p(x) = √ exp (− ), x ∈ IR, 2πσ. 2 2σ 2. where µ = IE(X) ∈ IR and σ. 2
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