# Tagged Questions

Transformation has many meanings in mathematics. If using this tag, add another tag related to the object being transformed. If there is a tag for your specific kind of transformations, use that one instead: e.g., (laplace-transform), (fourier-analysis), (z-transform), (integral-transforms), (rigid-...

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### Convolution Problem

while working on a signal processing problem i've reached to the following: So my aproach was: Am I doing something wrong? Is it valid Y(f)=[X(f) x H(f)]*W(f)=X(f) x [H(f)*W(f)] If you could ...
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### Construction of a Transformation of a Random Vector that Preserves Independence

Let $X_1, \dots, X_n$ be $n$ independent random variables, not necessarily normal. Let $Y_1 = \sum_{i=1}^{n}\alpha_i X_i$ a given linear combination of the random variables. Is there a known, "...
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### optimal monotonic transform: $\min_f (f(x)-y)^2$

Given two vectors of length $N$ denoted by $x_i$ and $y_i$, $1\leq i\leq N$, what is the monotonic transformation $f(x)$ that minimizes the overall distance $D=\sum_{i=1}^{N}{(f(x_i) - y_i)^2}$. Does ...
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### How do I find the Probability Function of this Transform?

Given the Probability Generating Function for a non-negative, integer-valued, R.V. $X$ as: $$g_X(t)=\log\left(\frac 1 {1-qt}\right).$$ How do I compute its Probability Function, $P(X=k)$? A step-...
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### Transformation Matrix for particular problem

I have a question regarding transformation matrices. I have two images both showing a table. I have coordinates of the corners of the tables, and now I want to apply a transform to 1 of the images so ...
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### Finding Equality around Axis of Symmetry

I have a particular function that for even numbers $m$ obeys the following equation: $$f_{m,n}\left(\frac{2}{m}-x\right)=(-1)^nf_{m,n}(x)$$ Now when I put in odd values for $m$ and plot the function,...
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### Inverse Laplace Transform by Partial Fraction Expansion

I've been trying to solve this partial fraction for a Laplace transformation but I can't. Is there any way to solve it? $$\frac{(s-t)^2}{((s-t)^2-1)((s+1)^2+4)}$$ Could somebody help, I've been ...
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### Measuring Image of a Set Using Jacobian Integral

Assume $T:\mathbb{R}^d \to \mathbb{R}^d$ is a differentiable mapping and $E$ be a measurable set. Show that $m(T(E))=\int_E |det(DT(x))|dx$. I am thinking I might use the following Theorem, but I ...
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### How to rotate points given in square grid?

I really hope you can see this picture. So My question is 1) If the figure is rotated 90 degrees counter clock wise about Point O, then: $$a. G to _________$$ $$b. _________ to P$$ How would i ...
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### Get the positions of a periodic system of labeled points in reference to another coordinate system

First of all, I'd like to apologize because I'm not familiar with the conventions (names and formats) used in the math community. The problem is the following, I have information about a Face ...
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### 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 transformed random variable $X = \sin(U)$. ...
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### How wil the parameters of a bi-variate normal distribution change if I rotate the x-y panel?

For a bi-variate normal distribution: If rho = 0, then the plot in x-y panel would look like: I'm wonder, if I rotate the ...
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### Particularly Problematic Spherical Polar Problem

The question is as follows: Using spherical polar coordinates, find the volume of the solid specified by R $\leq$ 3 and $0 \leq \theta \leq \frac{\pi}{3}$. I have two big questions about this ...
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I know that : $$f_X(x)=\cases{1 & x\in [0,1]\\0 & x\notin[0,1]}$$ Then: $$P(Y\leq y)=P(\frac{1}{X}-X\leq y)=P(X\leq\frac{1}{2}(\sqrt{y^2+4}-y))$$ as $$\frac{1}{x}-x=y\rightarrow x\frac{1}{... 1answer 28 views ### Elliptic Coordinates - Inverting the transformation The standard way to transform elliptic coordinates (\mu, \nu) \ to Cartesian coordinates (x,y): x = a \cosh(\mu) \cos(\nu) y = a \sinh(\mu) \sin(\nu) Is there any way to get the ... 2answers 30 views ### Find the coefficient of partial expansion \frac{2x+3}{(1-x)(1+0.5x+0.5x^2)} I want to decompose the equation:$$\frac{2x+3}{(1-x)(1+0.5x+0.5x^2)}=\frac{A}{1-x}+\frac{B}{1+0.5x+0.5x^2} I found $A$ by multiple both side with $1-x$ and plug $x=1$. However, it is so difficult ...
Let T:P3→P3 be the linear transformation such that $T(−2x^2)= −2x^2 − 2x$, $T(0.5x + 2)= 3x^2 + 4x−2$, and $T(2x^2 − 1)= 2x + 1$. Find $T(1), T(x), T(x^2)$, and $T(ax^2 + bx + c)$, where a, b, and c ...