Ben Chuanlong Du's Blog

It is never too late to learn.

The Unfair Wager Problem

Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!

https://projecteuler.net/problem=436

\(X_i \sim Bernoulli(p)\)

$$\bar{X}_n \dot{\sim} N(p, \frac{p(1-p)}{n})$$
$$[\bar{X}\pm C_{\alpha} \sqrt{\frac{p(1-p)}{n}}]$$
$$\frac …

Fewest Scalings to Identify the Fake Ball

Things on this page are fragmentary and immature notes/thoughts of the author. It is not meant to readers but rather for convenient reference of the author and future improvement.

8 balls, one fake 2 problems

Stick Breaking Paradox

Things on this page arefragmentary and immature notes/thoughts of the author. It is not meant to readersbut rather for convenient reference of the author and future improvement.

  1. dirichlet distribution, circle, unit, identical, mixing problem ...

Ratio of Boy to Girl

Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!

In a country, all families prefer to have boys. They will keep having baby until they have a boy. After a long time, what is the ratio of boys to girls …

Expected Time to Hit Zero

Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!

Let DU(0, n) be the discrete uniform distribution on 0, 1, ..., n-1. X_1 \sim DU(0, n) X_2 \sim DU(0, X_2) repeat this process until we get zero. What …