Mathematics
Pei-Lun Tseng's user avatar
Pei-Lun Tseng's user avatar
Pei-Lun Tseng's user avatar
Pei-Lun Tseng
  • Member for 6 years, 10 months
  • Last seen more than 2 years ago
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26
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7
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20
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9
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6
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2
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6
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31
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All Questions Answers
Score Newest
question
4
Compute $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2+(x-y)^2+y^2)}dxdy$
Apr 2, 2017
question
3
Show that there exists $g:D\rightarrow \mathbb{C}$ is analytic and one-to-one such that $(g(z))^2=f(z^2).$
Feb 9, 2017
question
3
Does $\lim\limits_{n\rightarrow \infty}E[X|F_n]$ exists a.s if $F_n$ is the $\sigma-$field generated by $Y_0,...,Y_n$ where $Y_n=X+W_n$.
Mar 10, 2017
question
3
Find the minimum value of $f$ on $\{(a,b,c)\in \mathbb{R^3}\mid a+b+c=1\}$ where $f(a,b,c)=\int_{0}^1 (a+bx+cx^2)^2dx$.
Apr 2, 2017
question
3
For $0<a<b$ and $n>0$, show that $\left|\int_{a}^b \frac{\cos x}{x^n}\,dx\right|\leq \frac{2}{a^n}.$
Apr 5, 2017
question
2
Prove or disprove $E[(X-E[X|Y,Z])^2]\leq E[(X-E[X|Y])^2]$
Mar 10, 2017
question
2
Show that $\lim\limits_{n\rightarrow \infty} P(S_n=k^2$ for some $k\in \mathbb{N})=0$
Mar 30, 2017
answer
2
Show that $\liminf_{n \to \infty} x_n+ \liminf_{n \to \infty} y_n \leq \liminf_{n \to \infty}(x_n + y_n)$
Mar 10, 2017
question
2
Find how many roots of $z^5+2z^2+7z+1=0$ lie inside $|z|=2$? How many are real?
Apr 4, 2017
question
2
If $z=a$ is not the removable singularity of $f$, show that $e^{f(z)}$ has essential singularity at $z=a$.
Apr 5, 2017

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