T. Eskin
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 Mar 23 comment homeomorphism from $\mathbb{R}^2$ to open unit disk. What is $f(0,0)$? Mar 20 reviewed Reject unbounded-operators tag wiki excerpt Mar 13 reviewed Approve Showing a queueing system is a Markov Chain Mar 13 comment Mean of a squared random variable Since the OP already expressed that he figured this out, I'll write it out here. Since $Var(X)=E(X^{2})-E(X)^{2}$ for any random variable $X$ regardless of the distribution, then there is a general rule, mainly $E(X^{2})=Var(X)+E(X)^{2}$. I.e. if $X$ has mean $\mu$ and variance $\sigma^{2}$, then $E(X^{2})=\mu^{2}+\sigma^{2}$. Mar 13 answered How to find the basis for Ker($T$) of $T:P_n(R) \rightarrow P_n(R)$ given by differentiation. Mar 13 comment Mean of a squared random variable @user322504 Great! Mar 13 comment Let $A$ and $B$ be square matrices of order n so that $AB = BA$. Prove $rank(A+B) \leq rank(A) + rank(B) - rank(AB)$. @matthew.j There are many more examples of $A$ and $B$ such that $AB=BA$. Neither of them have to be diagonal or identity matrices. Mar 13 answered Mean of a squared random variable Mar 13 comment Bounded sequence in metric space has convergent subsequence Bounded sequences don't have convergent subsequences in general. Take e.g. $d(x,y)=\min\{|x-y|,1\}$ on $\mathbb{R}$. It's a metric that gives the standard topology. Also, every sequence is bounded with respect to this metric but there are plenty of sequences on $\mathbb{R}$ that do not have convergent subsequences. Mar 13 comment Pointwise convergence V.S. Uniform convergence $f$ is zero everywhere except $f(0)=1$. Try forming an argument and if you come to some specific problems I'll explain what went wrong. But try it yourself first. Mar 13 comment Pointwise convergence V.S. Uniform convergence Yeah, exactly. The reason is that $\sup|f_k(x)-f(x)|=1$ for all $k$. But it obviously converges point wise Mar 13 comment Pointwise convergence V.S. Uniform convergence So you have to make the function zero if it gets negative values. So take for example $g_k = \max\{f_k,0\}$, where $f_k$ is as you wrote it. Then $f_k$ converges to the limit function that you want. Mar 13 comment Pointwise convergence V.S. Uniform convergence The functions are not defined properly. Right now, if $x\neq 0$, then $f_{k}(x)\to -\infty$ as $k\to\infty$. You have to cap the functions to zero if the values are negative. Mar 13 comment Is $\{e^{-kn}\sin(kn^2\pi)\}_{n=1}^{n=\infty}$ =$\{0\}_{n=1}^{\infty}?$ Is $k$ also an integer? Mar 13 comment Find the eigenvalues and eigenvectors of $A$ geometrically. @LosSiento. You reflect the vector. By multiplying the vector with this matrix it reflects the vector. Mar 13 reviewed Reject Infinite sets don't exist!? Mar 13 reviewed Reject Could someone help with the result of this double summation? Mar 13 comment You toss a fair die three times. What is the expected value of the largest of the three outcomes? @ConnorJames. Cool. Thanks for sharing. Mar 13 answered You toss a fair die three times. What is the expected value of the largest of the three outcomes? Mar 11 revised How do I find the set $\bigcup_{k = 2}^{10}A_k$ if $A_k = [k, 2k-1]$ deleted 2 characters in body
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