Phillip Nicol
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Binomial risk under absolute value loss: why a cauliflower?
Probability
If
\(X \sim \text{Binom}(n,p)\)
then the estimator
\(\hat{p} = X/n\)
satisfies
\(\mathbb{E}(\hat{p} - p)^2 = n^{-1}p(1-p)\)
, which is quadratic (and concave) in
\(p\)
.…
Dec 8, 2025
Phillip Nicol
Ratio of Cauchy: ChatGPT fails on this simple question
Probability
It is well known that the ratio of two independent standard normals
\(Z_1/Z_2\)
follows a Cauchy distribution. But what about the ratio of two (independent) Cauchy…
Feb 8, 2025
Phillip Nicol
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