In Casella and Berger (2002) I found a proof for the moment-generating function (mfg) of a lognormal distribution not being existent (see exercise 2.36 on...

I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is $$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \&g...

This question is admittedly pedantic, but I like my definitions precise. Tom Apostol, in his calculus book, defines a periodic function as follows. A func...

I need tricks or shortcuts to find the inverse of $2 \times 2$ and $3 \times 3$ matrices. I have to take a time-based exam, in which I have to find the in...

Consider $ABCD$ is cyclic quadrilateral, the intersection of $AD$ and $CB$ is $E$, $AB$, $CD$ is $F$; $AC$ and $BD$ is $I$. Prove that $O$ is orthocenter ...

$\newcommand{\Var}{\operatorname{Var}}$In this video is claimed that if the equation of errors in OLS is given by: $$u=y - X\beta$$ Then in the presence o...

Is it possible to calculate $\log_{10} x$ without using $\log_{10}$? I'm interested because I'm working with a framework that has some simple fu...

I have started to do this question, but not sure if I am on the right track or not (or even allowed in math) Can someone say if what I am doing is right?

The answers from the back of the book says the answers are $\pi/2$ and $3\pi/2$. I thought that you can use the double angle formula in this problem, but ...

Suppose that there is a hyperbola of the form $\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$. I would like to figure out an equation that describes tangent line to...