Ben Chuanlong Du's Blog

It is never too late to learn.

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 \(0\), \(1\), ..., \(n-1\). Define random variables as below.

$$X_1 \sim DU(0, n)$$
$$X_{i+1} \sim DU(0, X_{i …

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 …