For the Quadratic Form $X^TAX; X\in\mathbb{R}^n, A\in\mathbb{R}^{n \times n}$ (which simplifies to $\Sigma_{i=0}^n\Sigma_{j=0}^nA_{ij}x_ix_j$), I tried to...

Exercise 2.5 of Izenman's Modern Multivariate Statistical Techniques: Consider a hypercube of dimension $r$ and sides of length $2A$ and inscribe in ...

Wikipedia defines the notion of a pure set as follows: a hereditary set (or pure set) is a set whose elements are all hereditary sets. Why does this defin...

I just came across the example of the topologist's sine curve that is connected but not path-connected. The rigorous proof of the non-path-connectedn...

Assume $X_1, X_2, ..., X_n$ is a random sample of a uniform random variable $X$ on the interval $(0,\theta)$. What is the density function for $X$ and the...

Here I am referring to the notation $x \wedge y = \min \{ x,y \}$ and $x \vee y = \max \{ x,y \}$. These seem to reference the corresponding usages in log...

Like interpret the intercept and slope in a practical context of the data. For example, if I am given this fitted regression line $$Y\hat = -0.55 + 0.09X$...

How do you prove a triangle is equiangular with 5 steps? All I know is that triangle abc is equilateral? I need to prove it with a 2 column proof. These a...

I've run into a small problem while working through Enderton's Elements of Set Theory. I'm doing the following problem: Call a natural numb...

I'm currently self-studying some complex analysis. My background is limited: single- and multivariable calculus, linear algebra, introductory Fourier...