# Tagged Questions

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### Characteristic Function Inversion

I am studying the relationship / bijection between characteristic functions and CDFs. In particular, given a characteristic function $\phi$ it is posible to recover the cumulative density function ...
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### Possible values of characteristic functions (Fourier transforms)

Can a characteristic function $\varphi_{X}(u)$ from probability theory (the Fourier transform of a probability measure) ever equal zero for either any value of $x$ or any value of $u$? This has been ...
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### How to model a stochastic process, continuous in stepsize, which converges against a simple random walk?

I want to compute the probability distribution for a stochastic process with discrete number of steps, where each real value has a nonvanishing probability to be the next stepsize. And I want to ...
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### Quantifying the “flatness” of functions which are the Fourier transforms of positive functions

I have a question which I admit is a little cumbersome for me to try to state succinctly, and which I fear may not have a simple answer, but I figured I'd give it a shot. In broad terms, I'm trying to ...
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### Sum of Independent Variables = Uniform?

Is there a probability density (or measure), such that the sum of two such independent random variables is distributed uniform? In other words, what is the Inverse Fourier Transform of the ...
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### Finding $E(X^r\mid Y)$ of an exponential function

Let $(X,Y)$ denote a two-dimensional random vector with an absolutely continuous distribution with density function $$p(x,y) = \frac{1}{y}\exp(-y), \qquad 0 < x < y < \infty.$$ Find ...
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### Lower bound of Fourier transform

We know the Fourier transform of the Gauss-function: $\displaystyle\int_{\xi\in\mathbb{R}^d}e^{-\pi\, C\,|\xi|^2}e^{2\pi i \xi\cdot X}d\xi=C^{-d/2}e^{-\, \pi\, |X|^2/2}$ for any $C>0$. Then ...
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### Intregral of exponential of Shannon Entropy Function

Here I am going to ask a similar question as rde asked , that is what is the integral of exponential of entropy function. That is what is the value of $F[H(x)]=\int_{-1}^{+1} e^{ikH(f(x^2))} dx$ ...
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### How to use joint characteristic function to calculate characteristic function for single variables? [duplicate]

Possible Duplicate: probability question on characteristic function It is a problem in my practice exam. Defined on some common probability space, two random variables $X$, $Y$ have the ...