# All Questions

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### Expectation of non-negative random variable

Let $X$ be a non-negative random variable. In a proof for $E[X]=\int_0^\infty P(X>t)dt$ from the answer of this question, we use Fubini for the middle quality. Why do we need $X$ to be ...
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### A matrix transformation from R^4 to R^3 - linear algebra - how to find the image of a point

I'm trying to revise for an upcoming exam on linear algebra and have come across this question. I do not understand the line "the image of a point (x1, x2, x3, x4) can be computed from the defining ...
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### transition maps of a principal bundle are smooh

A smooth principal fiber bundle is a smooth fiber bundle $\pi: E \to M$ together with a Lie group $G$ and a fiber preserving right action $E \times G \to E$ which restricts to each fiber freely and ...
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### In projective geometry the dual of the cross ratio dual is an angle measurement?

I am trying to get my head around angles in projective geometry. I understand (more or less) the cross ratio and that it can be seen as an distance measurement. (for example in the Beltrami Cayley ...
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### Basis of $H^1(\Omega)$ which is orthonormal wrt. $L^2(\partial\Omega)$ inner product?

Let $\Omega$ be a domain with $\partial\Omega$ bounded. Is it possible to find a smooth basis of $H^1(\Omega)$ and $L^2(\Omega)$ which is orthonormal wrt. the $L^2(\partial\Omega)$ inner product? ...
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11) Assume a sorted array (A) of size n. Propose an algorithm for finding two elements x and y in A that minimize |x-y|. Your algorithm should run in O(n) time for full credit. (Note: |x-y| represents ...
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### Algorithm for vector space transformation [on hold]

In my text book I've got an example which is as follows: Create an algorithm which calculates coordinates of a point after a space transformation took place. Transformations may be scaling or ...
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### What is a non-decreasing sequence of sets?

What is a non-decreasing sequence of sets and how come it can have a limit? It appear in a probability theory book
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### How to answer the question “what is the domain of this function”?

Could you please help me understand and solve this problem about domain of function? All that is written for the question is: What is  the  domain of this function? $$2\sin\sqrt{2x-1}+1$$ ...
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### If we know $a^{1 / 2} + a^{-1/2}$, how can we calculate $a + a^{-1}$?

Someone could help me with this? Thanks so much! Knowing the value of $a^{1/2}+a^{-1/2}$, calculate $a+a^{-1}$.
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### How many 10-character strings can be formed using p characters [on hold]

Let $A = \{a_1, a_2, . . ., a_p\}$. In how many ways you can select 5 elements? Let $A = \{a_1, a_2, . . ., a_p\}$ is a set of $p$ symbols. In how many ways you can make codes consists of 10 symbols? ...