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Mathematics : Recent Questions and Answers (Page 149)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Proof of Lemma 5.1.5.3 in Jacob Lurie's HTT.

I am currently trying to understand the following proof in Higher Topos Theory.I am fine with almost all of the argument, except with...

Asked on 01/16/2021 by Robin Carlier

1 answer

What is the distribution of highest order statistics when the random variables follow exponential distribution with mean ??

Suppose $X_i sim exp(theta), i = 1, ldots, n$, iid.So the pdf is given by $f(x) = exp(-x/theta)/theta, x>0$.Now I need to find the distribution of...

Asked on 01/16/2021 by Alolika Ray

0 answer

Use a shortest-paths argument to prove a combinatorics identity

Let m and n be nonnegative integers, and let r, s, and t be nonnegative integers such that $r + s + t = m$. Use a shortest-paths argument...

Asked on 01/16/2021 by walterman

2 answer

Correlation between 2 random variables and $cos(theta)$ on vector space

I am studying from a book that asserts that the correlation between random variables $X$ and $Y$ is 0.8. And apparently this means that if $X$ and...

Asked on 01/16/2021

1 answer

Open set of the torus containing a point of the equivalence class?

Consider the torus defined by the quotient topology $S^1times[0,1];/sim$ where $sim$ defines the equivalence relation with $(x,0)sim(x,1)$ for any $xin S^1$. I need to characterise the...

Asked on 01/15/2021 by Edi

0 answer

Is only one SVD computation enough to perform PCA on a matrix and its transpose?

SVD is used in PCA in order to get the mapping to lower dimensions. Is it enough to perform only one SVD in order to get the PCA for the...

Asked on 01/15/2021 by Mark Ng

0 answer

Evaluate $int frac{dx}{(x-1)^{frac 34} (x+2)^{frac 54}}$

Given that $int frac{1}{(x-1)^{frac 34} (x+2)^{frac 54}}dx$ Let $(x-1)^{frac 14} = t$ So the integral becomes $$int frac{4}{(t^4+3)^{frac 54}} dx$$ How do I solve it further?...

Asked on 01/15/2021

2 answer

Minimum number of elements in ${0, 1, 2, dots, n}$ that add up to all of the elements of ${0, 1, 2, dots, n}$.

I was reflecting on the Goldbach conjecture when the following question came to my mind:Let $n$ be a natural number. What is the minimum number of elements you need...

Asked on 01/15/2021 by Arjuna196

2 answer

how to prove function is not invertible

If I have a function like $f(x) = x^2$ or $f(x) = sin(x)$ in the domain $[-infty infty]$, how can I prove that they are not invertible....

Asked on 01/15/2021 by deltaskelta

1 answer

Tangent circles in a rectangle

$ABCD$ is a rectangle with 4 semicircles tangent to each other. $AB$ is the diameter of a circle, $FC$, $GD$...

Asked on 01/15/2021

3 answer

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