Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 175

Is a generated field independent of the extension over which it is generated?

This sounds like a very basic question of field theory. It's probably a small detail, most authors and introductory sources to field theory seem to ignore it. Given a field...

Asked on 12/16/2020 by jam

1 answer

Limit of hypergeometric distribution when sample size grows with population size

Consider choosing $Mn/6$ balls from a population consisting of $M$ balls of each of $n$ colors (so $Mn$ balls in total). So the density function of...

Asked on 12/16/2020 by tc1729

2 answer

Arg of $(1-isqrt{3})^6$. Did I do it right?

Did I do it right? $(1-isqrt{3})^6$ module = $sqrt{1+3}=2$ $(1-isqrt{3})^6=2^6cdot(frac{1}{2}-frac{sqrt{3}}{2}i)^6$ $implies$ Arg = $frac{pi}{3}$...

Asked on 12/16/2020 by cocacola

3 answer

Is there closed formula to calculate the probability of beta distribution?

Part of my investigation of the properties of the beta distribution, I was trying to figure if for $Xsim Beta(a,b)$ is there a closed formula for $P(X>x)$, ...

Asked on 12/16/2020 by vesii

1 answer

Coloring Two Faces of an Icosahedron

Suppose that you have a solid regular icosahedron (a polytope with 20 sides all of which areequilateral triangles), and all the sides are white. (a) In how many ways...

Asked on 12/16/2020 by user826216

2 answer

prove that there is only one a, such: $y'(x)=y(x)^3+sin(x);y(0)=a$ and y(x) is a unique periodic solution

prove that there is only one real a, such:$y'(x)=y(x)^3+sin(x);y(0)=a$ which satisfies that y is a unique periodic solution.Find whether a is greater than 0 or smaller...

Asked on 12/16/2020 by user819065

0 answer

Proof that there are only two automorphisms of $mathbb{Q}(sqrt d)$ fixing $mathbb{Q}$

I have to proof that the only (field) automorphism of $mathbb{Q}(sqrt d)$ fixing $mathbb{Q}$ are $id$ and the conjugation $sigma$. I know for every such automorphism...

Asked on 12/15/2020 by HyperPro

1 answer

Find $lim_{xto 0} frac{sqrt{ax+b}-1}{x}=1$

My answer Let $sqrt{ax+b}=y$ Then$$lim_{yto sqrt b} frac{(y-1)a}{y^2-b}$$ Let $b=1$Then $$lim _{yto 1} frac{a}{frac{y^2-1}{y-1}}$$$$=frac a2 =1$$$$a=2$$ The answer is correct,...

Asked on 12/15/2020

3 answer

Improper integral of unbounded function over bounded interval

I'm asked to prove one of the properties of improper integrals for unbounded functions over bounded integrals. The problem is stated at follows:Let f,g:[0,a] $ to mathbb R$...

Asked on 12/15/2020 by Wykk

1 answer

representing of expectation for submatrices

Consider a matrix$$A=begin{pmatrix}a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} \a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26}...

Asked on 12/15/2020 by user4164

0 answer

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