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Questions Asked

kirbykirby:
Pathindependence of Complex Integrals?
…
 updated yesterday
 4 replies
 1 Medal
Mathematics

kirbykirby:
How can I label just one equation in an {aligned} environment?
 updated 2 days ago
 2 replies
 No Medals Yet
Mathematics

kirbykirby:
Finding the MLE under the null hypothesis:
 updated 8 days ago
 5 replies
 1 Medal
Mathematics

kirbykirby:
How to make every line start leftaligned in a LaTeX document?
…
 updated 8 days ago
 7 replies
 2 Medals
Mathematics

kirbykirby:
How to make every line start rightaligned in a LaTeX document?
 updated 9 days ago
 No Medals Yet
Mathematics

kirbykirby:
How can I add a tilde (~) under a letter in LaTeX?
 updated 10 days ago
 8 replies
 1 Medal
Mathematics

kirbykirby:
Is there a way to adjust the size integral sign automatically depending on "size" of the integrand?
 updated 11 days ago
 10 replies
 3 Medals
Mathematics

kirbykirby:
Integral:\[\int_0^{\infty}\frac{\cos t}{(t^2+1)^2}dt\]
(Note: this might need methods of complex integration).
 updated 19 days ago
 8 replies
 No Medals Yet
Mathematics

kirbykirby:
If \(X_1,\ldots,X_n\) is a random sample from a continuous distribution with pdf \(f_{\theta}(x)\). Why is the joint pdf of the order statis…
 updated 23 days ago
 3 replies
 1 Medal
Mathematics

kirbykirby:
Another complex integral:
Let \(0<a<2\). Show, using a keyhole contour, that \[\int_0^{\infty}\frac{t^{a1}}{t^2+1}dt =\frac{\pi}{2\sin(a\p…
 updated 26 days ago
 29 replies
 1 Medal
Mathematics

kirbykirby:
Complex integral:
Let \(\gamma: [\pi/2, \pi] \rightarrow \mathbb{C}\) be given by \(\gamma(t)=3e^{it}, \pi/2 \le t \le \pi\). Show that \[\…
 updated 28 days ago
 12 replies
 1 Medal
Mathematics

kirbykirby:
Let \(\gamma: [\pi/2, \pi] \rightarrow \mathbb{C}\) be given by \(\gamma(t)=3e^{it}, \pi/2 \le t \le \pi\). Show that \[\left\int_{\gamma} …
 updated 28 days ago
 No Medals Yet
Mathematics

kirbykirby:
I have in my problem that \(X_1,\ldots,X_n\) is a random sample from a distribution with probability density \(f(x; \theta)=\theta x^{\theta…
 updated one month ago
 6 replies
 1 Medal
Mathematics

kirbykirby:
Big O notation: How to simplify this:
\[\left(1+ \frac{1}{4n}+O\left(\frac{1}{n^2}\right)\right)^2\]
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 updated one month ago
 2 replies
 No Medals Yet
Mathematics

kirbykirby:
An iid sample \(X_1,\dots\,X_n\) have pdf \(f(x;\theta)=\theta x^{\theta1},\,\,\,\, 0<x\le 1, \,\,\theta >0\). The MLE is \[\hat{\theta}=\f…
 updated one month ago
 6 replies
 No Medals Yet
Mathematics

kirbykirby:
An iid sample \(X_1,\dots\,X_n\) have pdf \(f(x;\theta)=\theta x^{\theta1},\,\,\,\, 0<x\le 1, \,\,\theta >0\). The MLE is \[\hat{\theta}=\f…
 updated one month ago
 2 replies
 No Medals Yet
Mathematics

kirbykirby:
\[\int_{\gamma}\frac{z}{(z1)^{2014}}dz\], where \(\gamma\) is the diamond with vertices \(2, 2i, 2, 2i \).
 updated one month ago
 4 replies
 1 Medal
Mathematics

kirbykirby:
Parametric representation of the line segment in the complex plane from (2, 0) to (0, 2i).
 updated one month ago
 4 replies
 No Medals Yet
Mathematics

kirbykirby:
\[\int_{\gamma}\frac{1}{4z^21}dz\] where \(\gamma\) is the unit circle, \(z \in \mathbb{C}\).
 updated one month ago
 4 replies
 No Medals Yet
Mathematics

kirbykirby:
I have this change of indices:
\[\sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \frac{z^j}{j!} \frac{w^k}{k!} = \sum_{n=0}^{\infty} \sum_{k=0}^{n…
 updated one month ago
 6 replies
 1 Medal
Mathematics

kirbykirby:
I have this change of indexes in a double sum:\[\sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \frac{z^j}{j!} \frac{w^k}{k!} = \sum_{n=0}^{\infty} …
 updated one month ago
 No Medals Yet
Mathematics

kirbykirby:
Let \(f:\mathbb{C} \rightarrow \mathbb{C}\) be continuous and assume that \(f(z)=f(2z)\) for all \(z \in \mathbb{C}\). Show that \(f\) is co…
 updated 2 months ago
 14 replies
 2 Medals
Mathematics

kirbykirby:
If T~BIN(n, p), then find the expectation:
E[T(T1)...(Tk+1)]
 updated 2 months ago
 11 replies
 No Medals Yet
Mathematics

kirbykirby:
How can I find the expectation of the kth factorial moment, defined as E[X(X1)(X2)...(Xk+1)] where k=1, 2, ..., for a Poisson(theta) di…
 updated 2 months ago
 No Medals Yet
Mathematics

kirbykirby:
Using exp(iθ) = cos(θ)+ i sin(θ), show that
cos^2(θ) + sin(θ) = 1
 updated 2 months ago
 8 replies
 2 Medals
Mathematics

kirbykirby:
How to compute this sum?
\[\sum_{k=m}^{m+NM}k\frac{{M \choose {m1}}{{NM}\choose {km}}}{{N \choose {k1}}}\frac{Mm+1}{Nk+1} \] for \(N…
 updated 3 months ago
 6 replies
 No Medals Yet
Mathematics

kirbykirby:
Showing \(e^z\le 1\text{ if Re}(z)\le 0\), where \(z\) is a complex number.
 updated 3 months ago
 5 replies
 2 Medals
Mathematics

kirbykirby:
Probability/Random variables:
Assume all the random variables are mutually independent. Let \(S_n=X_1+X_2+...+X_{n1}+X_n\)
…
 updated 4 months ago
 No Medals Yet
Mathematics

kirbykirby:
Assume all the random variables are mutually independent. Let \(S_n=X_1+X_2+...+X_{n1}+X_n\)
Given this expression:
…
 updated 4 months ago
 No Medals Yet
Mathematics

kirbykirby:
If \(X\) and \(Y\) are 2 independent random variables, will functions of these random variables also be independent?
For example, if I h…
 updated 4 months ago
 22 replies
 1 Medal
Mathematics
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