Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 136

$ P (| X |> 1) = P (| X | <1) $

Let $X$ be a random variable following a uniform distribution over the interval $[-a, a]$ where $a$ is a constant greater than 1. If we have ...

Asked on 01/28/2021

1 answer

Sequentially open sets but not open

Can anyone think of an example of a topological space that admits sequentially open sets that are not open? A subset $Usubseteq X$ is called sequentially...

Asked on 01/28/2021 by T.I.

1 answer

Simplify $logleft(1+frac{x_i^2}{nu}right)$ with a $log(1+x)$ rule?

How can the following logarithm be simplified? Is there a $log(1+x)$ rule to use? $$ logleft(1+frac{x_i^2}{nu}right) = ?$$...

Asked on 01/28/2021

2 answer

Finding an Extremal for a function.

I need to find the extremals for the following function : $I(y) = displaystyle int_{x_0}^{x_1} dfrac{1 + y^2}{(y')^3} dx$ So, by Euler Lagrange Equations $I_{y}$ -$d/dx(I_{y'}) =...

Asked on 01/28/2021 by zeroflank

1 answer

Isomorphism between group of homeomorphisms where $X nsim Y$

This is question 7N #2 from Willard's General Topology, on p. 51.For any topological space $X$, let $H(X)$ denote the group ofhomeomorphisms of $X$ onto itself,...

Asked on 01/28/2021

2 answer

Basis of the field $E$=$mathbb{Q}(sqrt{6}i-sqrt{5})$.

Let's take a field $E$=$mathbb{Q}(sqrt{6}i-sqrt{5})$. I wanted to find a basis of $E$ as a $mathbb{Q}$-vectorspace.My first thought was to use the structure theorem for...

Asked on 01/27/2021 by questmath

3 answer

Limit points of the set ${frac {varphi(n) }n : nin mathbb{N}}$

Let $varphi(n)$ denotes the cardinality of the set ${a | 1le ale n, (a,n)=1}$ where $(a , n)$ denotes the gcd of $a$ and $n$....

Asked on 01/27/2021 by user-492177

1 answer

$forall epsilon >0,exists A in mathcal{A}$ such that $E subset A$ and $mu(A setminus E) < epsilon$

In a measure space $(X, mathcal{M}, mu)$ with finite measure, $mathcal{A} subset mathcal{M}$ is an algebra. We want to show that if set $E_i in mathcal{M}$ satisfies...

Asked on 01/27/2021 by user21

1 answer

Generalized Collatz: divide out by $2$’s and $3$'s, otherwise $5n+1?$

One direction of generalizing Collatz is, instead of dividing out by the smallest prime $2$, to divide out by the first two smallest primes $2, 3$ and then...

Asked on 01/27/2021 by Rivers McForge

0 answer

How is the Rodrigues formula $L_n^k(x)=frac{e^x x^{-k}}{n!}frac{d^n}{dx^n}(e^{-x}x^{n+k})$ derived?

I am trying to deduce the Rodrigues formula for generalized Laguerre polynomials $$L_n^k(x)=frac{e^x x^{-k}}{n!}frac{d^n}{dx^n}(e^{-x}x^{n+k})$$ but I have reached a point where I do not know how to proceed, my...

Asked on 01/27/2021 by Almhz

1 answer

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