May 12, 2021 · Chebyshev's inequality says that the area in the red box is less than the area under the blue curve $f (x)$. The only issue with this picture is that, depending on $\lambda$ and $f$, you …

Regarding Chebyshev's and Markov's inequality. What is the relation (if any) between them? Which one is more strict (and in which situation)? Is there an easy way to understand what they express (kind of …

Dec 8, 2018 · The height of a person is a random variable with variance $\\leq 5$ square inches. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample …

Apr 18, 2024 · I am trying to understand the proof of Chebyshev's association inequality in the book Concentration Inequalities: A Nonasymptotic Theory of Independence: Theorem 2.14 2.14 Let f f and …

Jun 1, 2015 · 3 I want to use Chebyshev interpolation. But I am a little confused for finding Chebyshev nodes. I use the following figure to illustrate my problem. Consider I have a vector of numbers I …

Jul 9, 2023 · Chebyshev's inequality looks a strange thing to use here as the distribution and values you see give a lot of information. Clearly $0 \le \theta \le 1$ as it is the parameter of a binomial distribution.

Mar 3, 2018 · Apparently the Chebyshev polynomials are those which minimize the Runge phenomenon, so this should mean that the Gauss-Chebyshev rule should be more accurate? Would …

Aug 7, 2024 · Chebyshev polynomials (of the first kind) are easily defined by $$ T_n (\cos \theta) = \cos (n \theta) $$ Is there a piece of literature that tries to extend this to multiple variables? For example: ...

Jan 9, 2024 · What distinguishes Chebyshev interpolation using Lagrange polynomials at Chebyshev points, and what advantages does it offer over traditional Lagrange interpolation with equispaced …

Jun 30, 2015 · It would be better to rephrase the question in more specific terms, like: "How to compute the Fourier-Chebyshev expansion of $\sin (x)$ and $\cos (x)$ over $ [-1,1]$?" - and add your …