Probability

2026-07-07

23 Birthday Problems

Solutions

Q1

a)

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

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24 Birthday Problems

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

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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.

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Logistic Regression

Here we aim to understand how exactly “Logistic Regression”, a method that seems only to be used for classification problems, is indeed a regression algorithm.

We will as per the trend thus far, detail closed-form and approximate solutions to the loss function on this page. Furthermore, we will see how this type of regression is still a member of the GLM (generalised linear models) family, and we shall witness the derivation of the loss function by assuming our data is Bernoulli distributed.

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Masters of Statistics

#Course CodeTitleOfferedPrerequisitesTermTypeTextbookNotes
1.COMP6713Natural Language ProcessingT1MATH1081,944426T1Electivena
2.FINS5513Investments and Portfolio SelectionT1,2,38750 program26T1Electivena
3.FINS5536Fixed Income Securities and Interest Rate DerivativesT2551326T2Electivenapricing, hedging, risk management. options, futures and swaps (int rate derivs)
4.MATH5856Introduction to Statistics and Statistical ComputationsT226T2Electivenarecommended for 5905
6.MATH5960Bayesian Inference and ComputationT32801/290126T3Elective
7.MATH5825Measure, Integration and ProbabilityT3U570526T3Electivenaimplicit prereq for 5835
8.MATH5905Statistical InferenceT1,2,3U5846,U585627T1Corena
9.COMP9518Advanced Machine LearningT2951727T2Electivena
10.MATH5845Time SeriesT227T2Electivena
11.MATH5855Multivariate AnalysisT327T3Electivena
12.MATH5835Advanced Stochastic ProcessesT1U582528T1CorenaDifficult. Requires an understanding of Real Analysis and Measure Theory
13.MATH5806Applied Regression AnalysisT228T2Electivenasplines, poisson / binomial regression
14.MATH5925Project (12uoc)T1,2,336UoC28T2Corena

new plan ATTACH

term (tentative)course codecourse nameUoC
27T1MATH5975Introduction to Stochastic Analysis6
27T1MATH5371Numerical Linear Algebra6
27T2COMP9418Advanced Machine Learning6
27T3MATH5960Bayesian Inference and Computation6
28T1FINS5513Investments and Portfolio Selection6
28T1MATH5905Statistical Inference6
28T2FINS5536Fixed Income Securities & Interest Rate Derivatives6
28T2MATH5835Advanced Stochastic Processes6
29T1MATH5845Time Series6
29T1MATH5925Project6
29T2MATH5825Measure, Integration and Probability6
29T2MATH5925Project6

rebellion plan

handbook: https://www.handbook.unsw.edu.au/postgraduate/programs/2026/8750?year=2026

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Mathematics for Machine Learning

credit for these solutions goes to: https://github.com/ilmoi/MML-Book

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