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7h
comment Strong induction MIT
You want us to solve the entire assignment for you? Unless you post specific questions from it with at least some effort on your part this question will end up closed.
7h
answered If $\{a_n\}$ converges to $A$, then $\{(a_1\cdots a_n)^{1/n}\}$ converges to $A$
7h
comment My MATLAB simulation shows that the Monty Hall probabilites are different… Why?
I'm confused by your code. You seem to be generating only two doors, not three.
8h
comment Number of connected components of an induced subgraph
Is there a way to calculate them? Yes, just calculate them. If $A_i$ and $A_j$ are in a connected component of the original graph, then they are in the same connected component of the subgraph. Are you maybe interested in the distribution of the number of connected components in the subgraph?
1d
answered Lifetime of light bulbs is modeled as a Poisson Process - using excel
1d
answered What happens when I convert a Taylor series into an integral?
1d
comment Does anyone know of a closed form solution to the following integral?
This doesn't converge for $m=2$, $n=0$, along with many other values.
1d
answered How do I find if a series of integers is (somehow) regular
1d
answered Question about the limits of definite integrals
1d
comment The pencils in a box of crayons always have the same color
Why should there be any pencils at all? The second step assumes you have $n+1$ crayons, not pencils.
2d
comment Particular form of the kernel of a positive matrix
@uranix: The new question isn't true, if I understand it correctly. Take a matrix whose kernal is spanned by $(1,1,-1,-1)^T$. Then $H$ will always have two negative numbers in the same column.
2d
comment Particular form of the kernel of a positive matrix
@uranix: There's no point for the $Q,\lambda$ stuff because the fact that $H$ has at most one negative entry in each row,column implies the existence of $Q$ and $\lambda$, just pick $\lambda$ to be absurdly large and $Q$ to be the permutation matrix which picks out the negative entries of $H$.
2d
revised Particular form of the kernel of a positive matrix
deleted 39 characters in body
2d
answered Particular form of the kernel of a positive matrix
2d
comment Can there be a unique function for $\int_{\frac{1}{n}}^n \sinh(x) \, dx$ when including parameters of $ 0 < n < 1 $
@AAron: The integral is valid for any $n\neq 0$, integer or otherwise. It's a fact that $\int_a^b \sinh(x)dx=\cosh(b)-\cosh(a)$. It's completely unclear what you're looking for.
2d
comment Least Squares estimate
This is not generally true unless the $y_i$ are normal random variables. Then this follows from the definition of the chi-square distribution: en.wikipedia.org/wiki/Chi-squared_distribution
Jul
4
comment Random matrices, eigenvalue distribution.
@mathreader: It's a theorem due to Girko and Bai for normal random variables, and was extended by Tao and Vu for more general random variables. See here for example: terrytao.wordpress.com/2007/08/23/… The theorem is not trivial to prove.
Jul
3
comment Random matrices, eigenvalue distribution.
This is basically Girko's law for complex matrices. The original law is for real random matrices. mathworld.wolfram.com/GirkosCircularLaw.html
Jul
3
answered Find the coefficient of $x^9$ in $(1+x)(1+x^2)(1+x^3)\cdots(1+x^{100})$
Jul
3
comment Show that $\lim_{x\to\infty} f(x) = 0$.
@Elimination: $\int_0^\infty f(x)dx=\lim_{n\rightarrow\infty} \int_0^nf(x)dx$ by definition. If you did have such an alternating situation, then the integral would clearly oscillate between two non-zero values as $n\rightarrow\infty$.