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What's the difference between a likelihood mass function plus a discrete chance distribution? 0
$begingroup$ Essentially, you gave the answer oneself: "infinity about infinity" is not defined Simply because it should be the results of limiting processes of various nature.
In other scenarios of divergent integrals or sequence, the regularized benefit and/or expansion rate (germ at infinity) or actions in a singularity can differ too or perhaps the variances can compensate for one another as in the example earlier mentioned.
Notice that someone may define "transfinite" similar to "Dedekind infinite" that's an abuse of terms in my opinion.
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$begingroup$ How can a beneficial random variable $X$ which never normally takes on the worth $+infty$, have expected price $mathbb E [X] = +infty$?
Examples include things like: in case you are researching calculus of genuine variables, you are likely using the prolonged genuine line; should you be quantifying the number of factors in a group, you're almost certainly utilizing the cardinal quantities.
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(the principal exception I know of will be the extended hyperreal line, which has a lot of infinite figures obeying the 'regular' guidelines of arithmetic, in addition to a set of additional numbers we contact $+infty$ and $-infty$ that have the largest magnitude of all infinite figures, and do not obey the 'normal' rules of arithmetic)
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