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As somebody used to say:

Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do research. Smokes some more.

The same. Except I do not smoke.


Jan
25
comment Assigning tables for Speed Networking session
"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level."
Jan
25
comment Markov chain doesn't sum up to 1
(Sorry but the answer was accepted.) A hint that something is wrong with your approach is that, correcting some mistypings in your question) it leads to $$P(Y_{n+1}=1\mid Y_n=1)+P(Y_{n+1}=2\mid Y_n=1)+P(Y_{n+1}=3\mid Y_n=1)=2.$$
Jan
25
comment what is the difference between event space and probability space?
It seems to me that you are in great need of definitions. Are you aware of the definition of a sigma-algebra?
Jan
25
comment what is the difference between event space and probability space?
Do you think {null set,{1},{2},{1,2}} is a sigma-algebra on S={1,2,3,4}?
Jan
25
comment Does a conditional normal distribution imply an unconditional normal distribution?
Even lecture slides (which can be quite reputable) available on the web and claiming this, would do.
Jan
25
comment Markov chain doesn't sum up to 1
Even more precisely, you are using $P(A\mid B\cup C)=P(A\mid B)+P(A\mid C)$. This identity is obviously wrong, in general and in the specific case at hand. (Unrelated: My guess is that you did not understand the posted solution, so why did you accept it?)
Jan
25
comment Markov chain doesn't sum up to 1
You seem to think that $P(A\cup B\mid C\cup D)=P(A\mid C)+P(B\mid C)+P(A\mid A)+P(B\mid D)$. Not so.
Jan
24
revised Central limit theorem with Lyapunov condition
deleted 2 characters in body
Jan
24
comment Central limit theorem with Lyapunov condition
"What am I doing wrong?" Nothing, since $\sqrt{1/(1-a_n)}\to1$.
Jan
24
comment Why is $\varphi\colon A^G\to A$ continuous?
Got something from the answer? If yes, why not accept it?
Jan
24
comment Why does $\lim_n T^{3n}\mu$ exist?
Yet another question left hanging?
Jan
24
comment What exactly does it mean for a measure to be translation-invariant?
Got something from the answer below?
Jan
24
comment Radius of convergence: Why is it $\geq 1$?
What happens there? Are you leaving the question in disarray?
Jan
24
comment Systems Theory - Complex Critical Point System
No, since $x_1(t)$ and $x_2(t)$ are real for every time $t$.
Jan
24
comment Does a conditional normal distribution imply an unconditional normal distribution?
"I have often seen it claimed that for scalar random variables $y$ and $x$, the conditional normal distribution $y|x\sim N(0,x^2)$ also implies the unconditional normal distribution $y\sim N(0,x^2).$" The first assertion is ok but the second is nonsense. What are your (numerous) sources? On the other hand, $x^{-1}y\sim N(0,1)$ is flawless provided $P(x=0)=0$.
Jan
24
comment Convergence of a recursive sequence of functions
*Please exchange $p\gt1/2$ and $p\lt1/2$ in my previous comment.
Jan
24
comment How come everyone says that you can't with in lottery because of statistics yet every single day I hear that someone has won?
Yeah, "the biggest unsolved paradox of modern mathematics" alone, would not be impressive enough.
Jan
24
comment Convergence of a recursive sequence of functions
A graphical approach, based on the graph of the function $g_p:x\mapsto1-p+px^2$ on the interval $[0,1]$, would yield the result directly. When $p\gt1/2$, $g_p$ is above the diagonal and meets the diagonal at $1$ hence $f_n(p)=g_p^{(n+1)}(0)\to1$ while, if $p\lt1/2$, $g_p$ meets the diagonal at $x_p=(1-p)/p$ hence $f_n(p)=g_p^{(n+1)}(0)\to x_p$. This approach has the dis/advantage of being direct and avoiding messy (irrelevant) computations. (Note that the question is obviously related to extinction probabilities for binary branching processes and that this context ought to be mentioned.)
Jan
24
comment Finding a strict Liapunov finction
"nonlinear programming techniques" Mwahaha... :-)
Jan
24
comment $ \sum_{n=1}^{\infty} \frac{{{n+1}}}{{{n}}}{a_n} $ is absolutely convergent.
Hmmm... Attempts?