Questions

Calculation of $sinh(ln(x+\sqrt{x^2+1}) $ => $x = 0$ Derivate of $ ln(x+\sqrt{x^2+1})$ => $\tfrac{1}{\sqrt{x^2+1} } $ arcsin^-1(x) = $\tfrac{1}{\sqrt{x^2 +1 } } $ Use the previous information:Le...

Let V be a vector space and suppose U1,…,Um are finite dimensional subspaces of V such that U1 + … + Um is a direct sum. Prove that U1⊕ … ⊕ Um is finite dimensional and dim(U1⊕ ... ⊕ Um) = dimU1 + … +...

Two points lie at random position on the border of a square of side length $L$. What is the probability that the distance $D$ between them is larger than $L$? Plese see the attached image below. I nee...

Let $(\alpha_n)_{n\in \mathbb{N}}$ be a sequence of non-zero real numbers such that $\sum_{n=1}^\infty \lvert \alpha_n \rvert^2 < \infty$. We consider the Riesz ProductBasically, I need to compute...

How is CART impurity cost function minimized?J(k,t_k) = \frac{m_{left}}{m}G_{left}+\frac{m_{right}}{m}G_{right}where G_{left/right} measures the impurity of the left/right subsetand m_{left/right } is...

If there is a pool of 2 Ms, 2 As, 2 Ts, 2Hs, and 1 X, Y, Z, how would you find the probability that if you drew 7 letter cards that you could spell Math from what you drew?

I've linked an image with the question on.

I've uploaded an image which contains the question.The answers are $-\frac{5\pi }{24} ,-\frac{\pi }{24},\frac{19\pi }{24},\frac{23\pi }{24} $ But I don't know how you get $\frac{19\pi }{24},\frac{23\p...

Image file contains question.

Image file contains question.

Determine an equilibrium temperature distribution (if one exists) for what value of B are there solutions? Explain physically$\frac{\partial u}{\partial t}=\frac{\partial u^2}{\partial x^2},u(x,0)=f(x...

So author explains how Hard Margin SVM works under the hood(as partially seen on image).But didn't explain what is the idea of minimizing \frac{1}{2}w^TwSo why do we have to minimize it? What is the i...

A line $\vec{L}$ has symmetric equations $\frac{5}{3}x-3 = \frac{4}{3}y + 1 = \frac{1}{3}z + 2$.The point P (0,-1,-2) does not lie on the line. Find the equation of the plane which contains both the l...

Given that\begin{vmatrix} a & b & c \\ 10d & 10e & 10e \\ g & h & i \end{vmatrix}=7, find the value of\begin{vmatrix} d & e & f \\ a-2g & b-2h & c-2i \\ 5g &...

My question is if you have a question like: Find the values of K for which $y=kx-3$ does not intersect $y=x^2-2x+1$To solve it my textbook says to do this.$x^2-2x+1=kx-3$ $x^2-(2+k)x+4=0$ Then we use...

Suppose $f(x) \in C^2[0,1]$ such that $f(0)=f(1)=0$, and $f(x)\neq 0$ on $(0,1)$. Prove that\int_0^1 \left| \frac{f''(x)}{f(x)} \right| dx \geq 4.

I’m pretty new to proof—based mathematics and so far I’ve noticed that one type of proof I seem to struggle the most with is proving an existence claim. Particularly, showing the existence of some obj...

The title explains it. Prove that : $ \sum_{k=1}^{\infty} {(-1)^k\rm e}^{-\hat{t} k^2} \geq \frac{2}{\pi}\ \sum_{k=1}^{\infty} \frac{(-1)^k}{2k-1}{\rm e}^{\frac{-\hat{t} (2k-1)^2}{4}}  $ for $\hat{t}&...

How do definite integrals give you the area under a curve? I understand how to find the area of a curve for something simple like $y = x^3 - 6x^2 +9x$ between 0 - 3 but my question is why does it work...

Continuation of https://matchmaticians.com/questions/qse0ka . Still struggling with understanding Bayesian statistics, so I need comparsion of MLE and Bayesian method(or whatever it is called) please....

A little disclaimer:I started learning ML and currently reading Ian Goodfellow's "Deep learning" and these are my first attempts to use my Statistics and Probabilities Theory knowledge, so some concep...

How to find derivatives of functions consisting of matrices and vectors? For example:f(x) =x^TA^TAxAs I understand A^TA can be treated as constant? How to treat x^TMy intuition tells me that somehow d...

Hello! I got referred to here by someone from the econometrics subreddit.I ran an experiment with a treatment and a control group. Treatment group voted under an electoral rule, where voters could cas...

Hi, I am doing a unit-fixed effects panel data analysis to examine the relationship between income and education for 26 regions over 9 years. My dependent variable is Gini, independent variables are p...

I understand how to calculate second order directional derivative. I want to get better understanding of the formula of it.So first order directional derivative of f(x,y) in direction of 'u' is:D_uf(x...