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Mar
23
comment Limiting distribution of $X_n1(|X_n|\le 1-\frac{1}{n})+n1(|X_n|>1-\frac{1}{n})$ if $X_n\sim Unif(-1,1)$ and are iid.
See Edit. $ $ $ $
Mar
23
revised Limiting distribution of $X_n1(|X_n|\le 1-\frac{1}{n})+n1(|X_n|>1-\frac{1}{n})$ if $X_n\sim Unif(-1,1)$ and are iid.
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Mar
23
comment Equation involving expectations of Levy processes
@saz No problem. :-)
Mar
23
revised Exponential Distribution with changing (time-varying) rate parameter
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Mar
23
answered Probability that there is an edge between two nodes in a random geometric graph
Mar
23
comment Probability that there is an edge between two nodes in a random geometric graph
Then this is not what you are asking in the question (and, when $r\leqslant\frac12$, you should find $c(r)\pi r^2$ for some $\frac14\lt c(r)\lt1$).
Mar
23
comment Riemann integration question
"What is the value of c in this case?" Please refer to your own post: here, the condition "$\forall c \in\ [a, b)$" means "for every $0\leqslant c\lt1$".
Mar
23
comment Probability that there is an edge between two nodes in a random geometric graph
Depends on what you want to do. The post does not suggest that you are asking for what the Edit tries to do. (By the way, the "Note" at the very end is wrong as well.)
Mar
23
comment Riemann integration question
But this is undefined at 1.
Mar
23
answered Riemann integration question
Mar
23
comment Probability that there is an edge between two nodes in a random geometric graph
Some (major) problems with the computation in your Edit: it does not take into account the boundaries of the square; it considers two points, not whatever number of points are thrown into the square; dimension arguments show that $r^4$ is absurd, for two points the thing should scale as $r^2$ when $r\to0$.
Mar
23
comment Laplace transform of gamma distribution
Integration by parts is unnecessarily complicated. The change of variable $u=(s+1/\theta)t$ and the condition that $L(0)=1$ for every Laplace transform yield readily the expression of $L_{k+1}(s)$. But yes, to get the recursion in the question, it might be necessary to take the long road of integration by parts.
Mar
23
answered Limiting distribution of $X_n1(|X_n|\le 1-\frac{1}{n})+n1(|X_n|>1-\frac{1}{n})$ if $X_n\sim Unif(-1,1)$ and are iid.
Mar
23
answered Theorem 6.11 of Rudin's Principles of Mathematical Analysis
Mar
23
revised How do I do this limit?
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Mar
23
comment How do I do this limit?
If $\to$ is $\sim$, the assertion holds.
Mar
23
comment How do I do this limit?
Is the first $\to$ actually a $\sim$ sign?
Mar
23
comment Help ! bizzare integral
Strange to write bizzare for bizarre and to use bizarre for standard.
Mar
23
answered How do I do this limit?
Mar
23
comment How do I do this limit?
Furthermore, in the "correct answer" you cite, the intermediate step is absurd since it depends on T and a limit when T goes to 0 cannot depend on T.