# All Questions

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### Why is the covariance a measure of how much two random variables change together?

In descriptive statistics, the empirical covariance of a point cloud $\left\{(x_i,y_i) : 1\le i\le n \right\}$ is defined as ...
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### Functions of 2 variables and applications to economics

Given the production function $Q := \sqrt K + L^2$, determine the optimal level of production and the relative demand of the two inputs capital $K$ and work $L$. The cost of a unit of capital ...
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### How do I count all values that satisfy X mod N=1 in the range [A,B]

I want to count how many values of x in range [A,B] give remainder of 1 when divided by N. Is there any formula I can apply?
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### Negation of a statement

So I am trying to prove a proposition. It goes like this Let there be $\emptyset\neq X\subset\mathbb{R}$ which is bounded from above. The next two statements are equivalent about $s\in\mathbb{R}$ ...
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### What makes a line “straight”?

In Euclidean space, there can be several definitions that makes a straght line: Line of shortest distance between two points Line that is linear, i.e with the points satisfying a linear equation ...
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### If A represents area of ellipse $3x^2+4xy +3y^2=1$ then the value of $\frac{3\sqrt{3}}{\pi}A = ?$

If A represents area of ellipse $3x^2+4xy +3y^2=1$ then the value of $\frac{3\sqrt{3}}{\pi}A = ?$ My approach : Since area of ellipse is $\pi ab$ where a is semi major axis and b is semi minor ...
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### Any suggestions for a Math book to revive my long lost math skills and knowledge?

Since I got my bachelor degree in computer science in 2005, I have rarely been in touch with or even need to do any significant mathematical calculations. I have consequently lost most of my math ...
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### CR Equations using Polar Form

I have a question to check whether following function is analytic or not using CR Equations. The question is f(z) = 1/(z-z^5) I just don't know how to start and ...
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### Ellipse 1 : E$_1 = \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 ( a > b)$ another ellipse 2 : $E_2$ which passes thru…

Problem : Ellipse 1 : E$_1 = \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 ( a > b)$ another ellipse 2 : $E_2$ which passes thru extremities of major axis of $E_1$ and has its foci at ends of its minor axis. ...
Hello I am studying group isomorphisms but I fail to check in a few cases whether two groups are isomorphic or not.for example in $S_3 \times Z_4$ and $S_4$ I have checked with ...