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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 $A_k = [k, 2k-1]$
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