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 Tenacious
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Jan
9
asked Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
Dec
16
awarded  Tenacious
Nov
21
comment Prove that Pb(x) = x / $||$x$||$ if $||$x$||$ $\gt$ 1 or x if $||$x$||$ $\leq$ 1.
Hint: Think of 2D space. Draw the norm ball, which is essentially a circle at the center in 2D. Take any point x in the plane. If you draw a line from the center to that point x, then this line will intersect with the exterior of the norm ball, what is that point?
Nov
8
awarded  Nice Answer
Nov
3
reviewed Approve Reflexivity of Relations
Nov
1
reviewed Reject Find the limit $\lim_{n\to\infty} \frac{(3n)! \, e^n}{(2n)!\,n^n\,8^n}$
Nov
1
reviewed Reject Find the limit $\lim_{n\to\infty} \frac{(3n)! \, e^n}{(2n)!\,n^n\,8^n}$
Oct
28
comment How to prove that if $\lambda_{\max}(A)\leq t\quad\iff\quad A\preceq tI$?
Hint: Prove the first implication $A \preceq tI \Rightarrow \lambda_{\max}(A) \leq t$. What does it mean for $tI - A$ to be positive semidefinite? (start from the definition)
Oct
26
comment Orthogonality of stochastic matrix
@AlgebraicPavel Thanks for the pointer! Theorem 4.1 looks very very useful!!
Oct
26
asked Orthogonality of stochastic matrix
Oct
19
awarded  Organizer
Oct
19
reviewed Reject Calculating factorial moment for distributions
Oct
18
comment Understanding Markov's inequality
Are you sure the first inequality would be true, if $\textrm{Range}(g) = [-\infty, 0]$?
Oct
17
revised Prove by induction: $\sum\limits_{k=1}^{n}\frac{1}{2^k}\tan\frac{x}{2^k}=\frac{1}{2^n}\cot\frac{x}{2^n}-\cot x,x\neq k\pi,k\in \mathbb{Z}$
Fixed notational bugs. k was being used for both induction as well index of the summation, making the propositions confusing. Fixed it by replacing k with m in the induction process.
Oct
17
revised Prove by induction: $\sum\limits_{k=1}^{n}\frac{1}{2^k}\tan\frac{x}{2^k}=\frac{1}{2^n}\cot\frac{x}{2^n}-\cot x,x\neq k\pi,k\in \mathbb{Z}$
fixed latex
Oct
11
answered Evaluate $\int_{0}^{\frac{1}{2}}\ x\cos(\pi x)\,\mathrm{d}x$
Oct
8
reviewed Reviewed Integration proof: sin(1/x) is integrable
Oct
8
revised Integration proof: sin(1/x) is integrable
Updated the question in the details section.
Oct
8
awarded  Custodian
Oct
8
reviewed Reviewed Really large birthday problem as a spacefaring question.