# Tagged Questions

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### Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?

In many applications, it is possible to derive an explicit expression for the Fourier transform of a random variable $X$ $$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$ ...
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### Probability generating function zero implies random variable is infinite

Let $V$ be a random variable supported on the nonnegative integers (including $\infty$) and $f(x) = \mathbf E x^V$ be the probability generating function. In our model $V$ is the number of visits to ...
Given a polynomial $P(x) = p_0 + p_1 x + p_2 x^2 + ... + p_n x^n$ with non-negative coefficients, is there a standard name for (the function of $p_1,...,p_n$ equal to) the variance of an ...
How can one solve the following recurrence relation? $f(n) = 1 + \frac{1}{2^n} \sum_{k = 0}^n {{n}\choose{k}} f(k)$ $f(0) = 0$ As it happens, I can show $f(n) = \Theta(\log n)$ through other means ...