Mathematical expectation 1

by Tricky123, May 11, 2025, 9:51 AM

X is continuous random variable having spectrum
$(-\infty,\infty)$ and the distribution function is $F(x)$ then
$E(X)=\int_{0}^{\infty}(1-F(x)-F(-x))dx$ and find the expression of $V(x)$

Ans:- $V(x)=\int_{0}^{\infty}(2x(1-F(x)+F(-x))dx-m^{2}$

How to solve help me

probability and stats

Japanese high school Olympiad.

by parkjungmin, May 11, 2025, 5:25 AM

It's about the Japanese high school Olympiad.

If there are any students who are good at math, try solving it.

Attachments:

Roots of a polynomial not in the disc of unity

by Fatoushima, May 11, 2025, 1:48 AM

Show that the polynomial $p_n(z)=\sum_{k=1}^nkz^{n-k}$ has no roots in the disc of unity.

This post has been edited 1 time. Last edited by Fatoushima, Today at 1:48 AM

algebra

complex analysis

Japanese Olympiad

by parkjungmin, May 10, 2025, 6:51 PM

It's about the Japanese Olympiad

I can't solve it no matter how much I think about it.

If there are people who are good at math

Please help me.

Attachments:

Hello, I'm a math Olympiad question for a Japanese high school. I'm asking here

by parkjungmin, May 10, 2025, 6:41 PM

This is very difficult, can anyone solve it?

The percentage of correct answers is low

Attachments:

D1029 : A story of equivalent and increasing sequence

by Dattier, May 10, 2025, 5:47 PM

Let $(a_n) \in (\mathbb R^*_+) ^\mathbb N$ an increasing sequence, with $\forall (b_n) \in (\mathbb R^*_+) ^\mathbb N$ , if $\lim \dfrac {a_n}{b_n}=1$ then $(b_n)$ increasing, from a certain rank.

Is it true $\exists M >1, \exists N \in \mathbb N, \forall n>N, \dfrac {a_{n+1}}{a_n} \geq M$ ?

This post has been edited 1 time. Last edited by Dattier, Yesterday at 6:29 PM

real analysis

Sequences

Double integrals

by fermion13pi, May 10, 2025, 1:58 PM

Evaluate the double integral by converting to polar coordinates:

$\int_0^1 \int_{x^2}^x (x^2 + y^2)^{-1/2} \, dy \, dx$
Change the order of integration and then convert to polar coordinates.

analytic geometry

calculus

integration

D1028 : A strange result about linear algebra

by Dattier, May 10, 2025, 1:49 PM

Let $p>3$ a prime number, with $H \subset M_p(\mathbb R), \dim(H)\geq 2$ and $H-\{0\} \subset GL_p(\mathbb R)$ , $H$ vector space.

Is it true that $H-\{0\}$ is a group?

Integration Bee Kaizo

by Calcul8er, Mar 2, 2025, 3:42 AM

Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!

Attachments:

Integration_Bee_Kaizo.pdf (167kb)

calculus

integration

Marginal Profit

by NC4723, Dec 11, 2015, 9:38 PM

Please help me solve this

Attachments:

marginal profit

calculus

algebra

Submit

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math_exploration

by Tricky123, May 11, 2025, 9:51 AM

by parkjungmin, May 11, 2025, 5:25 AM

by Fatoushima, May 11, 2025, 1:48 AM

by parkjungmin, May 10, 2025, 6:51 PM

by parkjungmin, May 10, 2025, 6:41 PM

by Dattier, May 10, 2025, 5:47 PM

by fermion13pi, May 10, 2025, 1:58 PM

by Dattier, May 10, 2025, 1:49 PM

by Calcul8er, Mar 2, 2025, 3:42 AM

by NC4723, Dec 11, 2015, 9:38 PM