How to calculate Probability of "Ranking"?
I took a course with other 10 students. After the final exam, the professor reported statistical result of scores to us: 1. The range of score: 46~98; 2. ...
Apr 13, 2026 1 VIEWS
Topic: General
5104 Articles 
Derivative of sinc function
How to show that function $\left(\operatorname{sinc}{x}\right)^{n}=\left\{\dfrac{\sin\left(x\right)}{x}\right\}^{n}$ is infinitely differentiable at $0$?
Apr 13, 2026 1 VIEWS
Adjacent edges in graph theory
May be a foolish question, but why is it always being said that "Two non-parallel edges are said to be adjacent if they are incident on a common vertex." ...
Apr 13, 2026 3 VIEWS
Transformation of variables for a non-monotonic function
Question: Let $U \sim \mathrm{Unif}(−α, α)$ follow the uniform distribution on the interval $(−α, α)$ for some parameter $α > 0$ and consider the trans...
Apr 13, 2026 1 VIEWS
What is the use of modulus in complex number?
The modulus of the complex number $z = a + bi$ is denoted by $|z|$ and is given by $|z| = \sqrt{a^2+b^2}$. What is the meaning of this? What is a modulus?
Apr 13, 2026 1 VIEWS
Integral of $\sqrt{1+\tan^2x}$ [duplicate]
Possible Duplicate: Ways to evaluate $\int \sec \theta d \theta$ I'm having a bit of a problem with an integral. The original problem was the length ...
Apr 13, 2026 1 VIEWS
When does trace and determinant of a 2 x 2 matrix equal each other? (Linear Algebra)
Background Information: I am new to linear algebra, and I recently came across this homework question that I am confused about. I appreciate any explanati...
Apr 13, 2026 1 VIEWS
Total variation distance, $L^1$ norm
Total variation distance is a measure for comparing two probability distributions (assuming that these are unit vectors in a finite space- where basis cor...
Apr 13, 2026 1 VIEWS
Calculating P(A>B), where A and B are normal distribution
In the problem we have that $A \sim N(7, 11/60)$ and $B \sim N(7.3, 7/20)$ and the question is what is the probability that $A$ gives a higher value that ...
Apr 13, 2026 1 VIEWS
Extrema of function with two variables
Given the function $f(x, y) = 3x^2y − y^3 − 6x$ Find the local extrema of $f(x, y)$. Firstly I find the partial derivitives, namely: $fx'=6xy-6, fxx&...
Apr 13, 2026 1 VIEWS
What does rate of change actually mean?
If we have a function, say, $y=x^2$, then $dy/dx=2x$. Now $y=1,4,9,16...$ for $x=1,2,3,4...$ and $dy/dx=2,4,6,8...$ for $x=1,2,3,4...$ Now as $dy/dx$ repr...
Apr 13, 2026 1 VIEWS
How to convert the general form of ellipse equation to the standard form?
How to convert the general form of ellipse equation to the standard form? $$-x+2y+x^2+xy+y^2=0$$
Apr 13, 2026 2 VIEWS