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If some maximum likelihood estimator (MLE) turns out to be unbiased (which does not necessarily holds), then does it achieve the Cramer-Rao lower bound (C...
As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "tex...
I thought $$\arctan(1) = \dfrac{\arcsin(1)}{\arccos(1)}$$ Sin hits 1 at $\pi/2$, and Cos hits 1 at $0$ and $2\pi$ So $\dfrac{\arcsin(1)}{\arccos(1)} = \df...
I'm reviewing algebraic topology, in particular the Kunneth Formula. I can't find online or in my book (by Hatcher) an explanation for how to ca...
Question: Find the solution of the heat conduction problem $$ \begin{cases} U_{xx} =4U_t , 0 < x < 2, t>0\\ U(0,t)=0, U(2,t)=0, t>0\\ U(x,0)=2...
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Write $\cos(x)$ in terms of $\sin(x)$ if the terminal point $x$ is in quadrant IV. I know $\cos^2(x)$ $= 1-\sin^2(x)$. And I know that cos is positive in ...
I was trying to find the integral of $\frac{\sin x}{x}$ recently, and nothing I tried appeared to get me any closer to a solution, so I looked it up and a...
Where $\phi, \psi$ are variables over formulas, are there logics for which we have either (or both) of $(1)$ and $(2)\thinspace$? $$(1) \hspace{0.5cm}(\ph...
I'm reading this pdf about lattices and there's this section where it talks about Gram-Schmidt Orthogonalization for a basis of a lattice. I kno...
