Probability · Maths EE idea · Accessible
Birthday problems beyond birthdays
A research question to start from
How many people are needed for a shared birthday with given probability, and how does the answer change for non-uniform birthdays or triple matches?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A famous problem, generalised in directions where you do the mathematics.
Mathematics you would need
- Complementary counting
- Approximations with eˣ
- Non-uniform distributions
- Simulation as a check
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Derive the exact result and an approximation.
- Prove that non-uniform birthdays make a match more likely (for small cases, then generally).
- Estimate the triple-match number.
Scope and difficulty
Accessible. Accessible; the non-uniform proof gives depth.
Pitfalls
- Only the classic case.
- Approximations without error discussion.
Where to start reading
Search a library catalogue or a university's open lecture notes for: birthday problem non-uniform distribution proof; approximation e^-n^2/2N. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).