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### Cramer-Rao bound for randomized estimator

As is well known, the Cramer-Rao bound (or information inequality) sets a lower bound on the variance of estimators of a parameter. Consider the case when the parameter is a scalar, the estimator is ...
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### Number of samples needed as input to Bernoulli factory

Let $\{X_i\}$ denote an i.i.d. sequence of Bernoulli variables with parameter $p$. A Bernoulli factory is a procedure that generates events with probability $f(p)$ using the observations $\{X_i\}$, ...
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### Another name for coin-flipping polynomials

In his paper Functions arising by coin flipping (section 4), Johan Wästlund coined the term "coin-flipping polynomial" for polynomials that arise in connection with observing a finite number of coin ...
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### Joint distribution from multiple marginals

Consider an experiment consisting of a repeated trial with two random Bernoulli (=binary) variables, A and B. Each trial consists of multiple outcomes for both A and B. Each trial has the same number ...
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### a function of Bernoulli variables?

Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two ...
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### Rigorous proof of the duality of Coupon collector's problem and Occupancy problem

We have $k$ different types of coupons (with replacement).If we collect at least $l$ different coupons, we win a prize. We can only afford to collect $m$ coupons. Let's say we take all those $m$ ...
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### Mean occurrences of letters in complete strings given by a Bernoulli scheme

Suppose one has an alphabet of $K$ letters, from which we draw sequentially letters; assume that the $n$-th letter occurs with a fixed probability $p_n$ independently of the others and of the previous ...
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### Generating Bernoulli Correlated Random Variables with Space Decaying Correlations

Hi, I have a set of N objects randomly distributed in a 2D physical space. Each object (i) generates a bernoulli random number (0 or 1) based on a marginal probability Pr(xi = 1) = p. These objects a ...