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like learning everything


12h
revised Power (monomial) form conversion to Chebyshev form
edited title
12h
comment Power (monomial) form conversion to Chebyshev form
Maybe the orthogonality of Chebyshev polynomials will help, at least when you allow to do numerical integration.
14h
revised Prove that this statement about A and B is true.
deleted 1 character in body
14h
revised Prove that this statement about A and B is true.
added 10 characters in body
14h
answered Prove that this statement about A and B is true.
15h
comment $\tan(z)$ with residue theorem
@ELEC by the definition of derivative.
16h
comment How to show that e.g. $E(\mathbf{w}) = \ldots \Rightarrow \frac{1}{2}(\Phi\mathbf{w} - \mathbf{t})^T(\Phi\mathbf{w} - \mathbf{t}) $
$x$ is a row vector, $y$ is a column vector, how do you define the product $xy$?
16h
answered $\tan(z)$ with residue theorem
16h
reviewed Approve suggested edit on Relationship between $m(E\backslash F) < \epsilon$ and $m(E)-m(F) < \epsilon$
16h
comment Kolmogorov zero-one law in continuous time?
@Frank It seems to be that with probability $0.5$, $\limsup X_t = a + 1$ and with probability $0.5$, $\limsup X_t = a - 1$
17h
comment Kolmogorov zero-one law in continuous time?
How about taking $X_t = a -1, \forall t$ with proba $0.5$ and $X_t = a+1, \forall t$ with proba $0.5$?
18h
comment Integral with residues
@ELEC yes, your mind follows the right way
18h
comment Integral with residues
@ELEC yeah, if your computation of derivative is right, a typo: the order of derivative is $k-1$ not $k$
19h
answered Integral with residues
22h
comment The operator Tf(x)=1/x∫f(t)dt on L2 is not compact
What have you tried?
22h
comment How to show this series diverges
Use Cauchy condensation test
22h
comment which of the following is sufficient for $\displaystyle \lim_{n\to \infty} \frac{a_n}{b_n}=1$?
For 1, take $a_n = \frac{1}{n}$ and $b_n = \frac{1}{n^2}$. For 5, take $a_n =-1, b_n = 1$
23h
comment antithetic sampling
@Jackie you decide what kind of random variable $X$ is, then you know its density, no?
1d
comment antithetic sampling
@Jackie the normal distribution is symmetric with respect to $0$. I think you just need to draw a graph to see in the plane $R^2$, if two points $(x_1,y)$ and $(x_2,y)$ are symmetric w.r.t the vertical line $x=a$, how to write $x_2$ in terms of $x_1$ and $a$?(answer: $x_2 = 2a - x_1$)
1d
comment antithetic sampling
@Jackie When symmetric with respect to $a$, when $X$ and $2a-X$ are of the same distribution. It's ok to take limit of $f(x)$ under some regularity conditions, but if the limit of $X$ is $[0,1]$, how can it be symmetric w.r.t $\frac{2}{5}$?