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Distribution of an angle between 3 normally distributed 2D points

Example image Given 3 normally distributed points in 2D space, what would the distribution of the angle $alpha$ between the three points be & can it...

Mathematics Asked by simejanko on 2 years ago

Relation between number of edges and the sum of number of vertices of degree k

Let P be a polyhedron and let G be its associated graph. Suppose P has Vvertices, E edges, and F faces. For each k, let $V_k$ be the...

Mathematics Asked by Dang Dang on 2 years ago

About basis of vector space of polynomial degree less than n

Let $r in mathbb{R}$ be an arbitrary real number. Show that $beta=left{1, x-r,(x-r)^{2},(x-r)^{3}, ldots,(x-r)^{n}right}$ is a basis of $P_{n}(mathbb{R})$. I know that if I can show this...

Mathematics Asked on 2 years ago

Dependent Simultaneous Equations

My maths TB says: For the simultaneous equations, $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ if $dfrac{a_1}{a_2} = dfrac{b_1}{b_2}...

Mathematics Asked on 2 years ago

What is the pdf of $frac{|x-y|}{(x+y)(2-x-y)}$ when $x,y$ are i.i.d uniform on $[0,1]$?

If $x,y$ are i.i.d uniform random variables on $[0,1]$. I know that the PDF of $|x-y|$ is: $$f(z) = begin{cases}2(1-z) & text{for $0 < z...

Mathematics Asked on 2 years ago

Example of Separable Product Space with cardinality greater than continuum?

In Willard, it's given that, for Hausdorff non-singleton spaces -$prod_{alphain A}X_alpha$ is separable iff $X_alpha$ is separable $forallalphain A$ and $|A|lemathfrak{c}$From reading the proof, I found...

Mathematics Asked on 2 years ago

find $f(n)$ that isn't little $o(n^2)$ and isn't $w(n)$

im having a problem with a question that tells me to find $f(n)$ so that $f(n) neq o(n^2)$ meaning also that $lim_{rightarrowinfty} frac{f(n)}{n^2} neq 0$ and ...

Mathematics Asked by Yuval Eliav on 2 years ago

I need help with Dudley problem 4.2.6

Theorem 4.2.8 in Dudley's Real Analysis and Probability states:Given a set $X$, a measurable space ($Y$, $mathcal{B}$), and a function$T$ from $X$ into ...

Mathematics Asked on 2 years ago

Point of intersection of pair of straight lines

We have our general equation is second degree in two variables:$ax^2+2hxy+by^2+2gx+2fy+c=0$ Let's say this represents a pair of straight lines Our professor told that we could find the...

Mathematics Asked by DatBoi on 2 years ago

Find the area between $f(x) = x^2+3x+7 $ and $g(x) = xe^{x^3+4}$ for $x in [3,5]$.

Calculate the area between the two functions, $f(x)$, $g(x)$, for $x in [3,5]$.$$f(x)=x^2+3x+7$$$$g(x)=xe^{x^3+4}$$To determine the area between the functions I used the formula...

Mathematics Asked on 2 years ago

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