Probability

Solutions#

Q1#

a)#

We use the update rule \[x_{n+1} = x_n - \frac{f(x_n)}{f’(x_n)}\]

As is tradition, the prize pool has increased (to $300 this year).

I have collapsed first and second place into a winner-takes-all arrangement (c’est la vie).

Furthermore, there are additional changes to the structure of this Game:

1. you must now pass the problem set to be awarded the prize money;
2. you may submit your solutions to the problem set at any point in the future;
3. if you plagiarise work, I reserve the right to ban you from all subsequent competitions — grim trigger
4. the problem and solution set will now be courteously supported by MathJaX, TikZ, and my own JavaScript
   • the problems can be found here, whilst the PDF can be found here and here (embedded).
   • my solutions will be available from the start of 2026; by viewing them you forfeit the prize money
5. Good luck!

PDF#

Links#

• Submission link
• List of Past Winners

Structure#

Most notably, the structure from this year has changed. Instead of just offering a single PDF and then writing up solutions on this site, the problems themselves are accessible from below and once 2025 transpires, my solutions will be available as toggled nested environments.

manufactured by amazon!

there is also a corresponding solution manual which I have found

Worked solutions to all 203 exercises live at Solutions to Rosenthal’s A First Look at Rigorous Probability Theory.

This blog post has been created to convince you that real-world probability, is in fact Bayesian probability.

Anyone who believes that a frequentist approach is superior may be correct (for that particular example), but it must be said that the Bayesian framework is a superset of this naive and trivial card-playing model of probability.

We are no longer trying to determine the probability of landing a double-six dice roll, and rather we are trying to figure out what the probability is that Mia (our cat) will be waiting for us on the porch when we get home.