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| bio | website | |
|---|---|---|
| location | ||
| age | 24 | |
| visits | member for | 1 year, 1 month |
| seen | Apr 8 at 8:09 | |
| stats | profile views | 13 |
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Sep 24 |
awarded | Commentator |
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Sep 24 |
comment |
What is the relevance of the supremum in this question? @dukenukem Yes, since you are considering continuous functions on a closed and bounded interval, taking the max is the same as taking the supremum (this is the extreme value theorem). |
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Sep 24 |
comment |
Determining if this set defines a metric over and open interval? Yes, for both questions there is a problem of integrability (that is, $d(x,y)$ could be infinite). However, unboundedness of $f$ or $g$ is not a problem per se: there are unbounded but integrable functions (on both $(0,1)$ and $\mathbb{R}$). |
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Apr 7 |
awarded | Organizer |
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Apr 5 |
comment |
Deducing probability from limited statistical data (exercise) "Obviously" only given monotonicity: in the Brave New World $a$ would be higher than both $p$ and $q$ ("Youth almost unimpaired till sixty, and then, crack! the end."). $\frac{p+q}{2}$ is a good guess but probably not the best one: it interpolates linearly, while something like an exponential distribution seems more appropriate. In what type of math course were you given this exercise? |
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Apr 5 |
comment |
Deducing probability from limited statistical data (exercise) Assuming the probability of living 15 more years is monotonic in age, we can bound the required probability between $p$ and $q$. I don't see how you can be any more precise than that. |
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Apr 4 |
comment |
Show $f \in L^p$ implies there is a set $E$ and a function $g$ for which $f=f\chi_E+g$ with $m(E)<\infty$ and $|g|\le 1$ Yes, precisely. |
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Apr 4 |
comment |
Show $f \in L^p$ implies there is a set $E$ and a function $g$ for which $f=f\chi_E+g$ with $m(E)<\infty$ and $|g|\le 1$ You are practically done! Just choose the right $g$... hint: it "complements" $f \chi_E$. |
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Apr 4 |
comment |
About probability By the way, don't put "Solved" in the title, but instead accept my answer (if you find it acceptable, of course). |
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Apr 4 |
comment |
About probability You're welcome, but you really need to be more precise with your notation: $a_1$ is the event (or rather $\{a_1\}$ is), which is very different from its probability $P(\{a_1\})$. |
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Apr 4 |
answered | About probability |
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Apr 4 |
answered | Pointwise convergence counter example. |
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Apr 1 |
revised |
Probability of second order equation with real coefficients to have real solutions? added 15 characters in body |
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Apr 1 |
awarded | Supporter |
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Apr 1 |
comment |
Integration of non-negative functions (Originally an answer; transforming into comment now that I have enough reputation.) It also holds when the $F_k$ are not disjoint; of course in that case we must have $a_k \neq b_k$. For example $\phi = \chi_{[0,1]}$ can have non-standard representations $\chi_{[0,1/2)} + \chi_{[1/2, 1]}$ (disjoint $F_k$ but non-distinct $b_k$'s) and $\frac{1}{3}\chi_{[0,1]} + \frac{2}{3}\chi_{[0,1]}$ (distinct $b_k$'s but overlapping $F_k$). |
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Apr 1 |
awarded | Teacher |
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Apr 1 |
answered | Final Question(For Now) On Basics Limit Arithmetics |
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Apr 1 |
awarded | Editor |
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Apr 1 |
revised |
Probability of second order equation with real coefficients to have real solutions? Added LaTeX |
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Apr 1 |
suggested | suggested edit on Probability of second order equation with real coefficients to have real solutions? |
