I have a matrix $A$ that is like this: \begin{equation} A = \pmatrix{ 1 & 2 & -3 & 1 & 5 \\ 1 & 3 & -1 & 4 & -2 \\ 1 &...

A transition matrix $P$ is said to be doubly stochastic if the sum over each column equals one, that is $\sum_i P_{ij}=1\space\forall i$. If such a chain ...

Recently I've been reading "The Wild Book" which applies semigroup theory to, among other things, chemical reactions. If I google for mathematics and...

Here's the problem. We have a random variable X that follows a Poisson law. If we take the log of this variable, what are the first two moments (mean...

I understand that the trace of the projection matrix (also known as the "hat" matrix) X*Inv(X'X)*X' in linear regression is equal to the rank of...

Q&A for people studying math at any level and professionals in related fields

Suppose point $C$ is directly above point $B$ of $\overline{AB}$. $|\overline{AB}| =2$, and the distance from $C$ to $B$ is $1$. How can I find the averag...

For example, if there are 50 boys in a school and the total number of students is $200$ then, for finding percentage of boys why do we do like this, $\lef...

Show that the surface area of a cone in terms of it’s height and radius is $\pi a \sqrt {a^2+h^2}$ by considering how a sector of a disc radius r angle $\...

Littlewood’s first principle says that each measurable set E of finite measure is nearly a union of finitely many open intervals. However, if the G for wh...