My requests and open questions on probability and function approximation

[peteroupc]

The following lists requests and open questions on some of the articles in this site. Can you help answer any of these? Answers to them will greatly improve my articles on this repository.

• Requests and open questions.
• Open questions on the Bernoulli factory problem.
• Other open questions on probability.

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The following are links to my questions on MathOverflow and other Stack Exchange sites.

Approximation of continuous functions:

• Polynomials that converge to a Bernoulli factory function
• Explicit and fast error bounds for approximating continuous functions
• Concave functions: series representation and converging polynomials
• Conjecture on consistent monotone sequences of polynomials
• Holtz method for polynomials that converge to a Bernoulli factory function

Simulations:

• Relatively simple simulations that succeed with an irrational probability
• Probabilities arising from permutations
• From coin flips to algebraic functions via pushdown automata
• Probability distributions computable by pushdown automata
• From biased coins, and nothing else, to biased coins
• From biased coins to biased coins, as efficiently as possible

Randomized estimation and others:

• Estimating f(E(X)) with a guaranteed error performance
• Checking if a shape covers a box
• A generalized randomized mean estimate based on the Chebyshev inequality
• https://math.stackexchange.com/questions/4697391/bounded-variation-of-derivatives-when-fitting-a-function-from-one-interval-into