5,652 reputation
52142
bio website
location California
age
visits member for 3 years, 8 months
seen Oct 20 at 19:19

A mediocre professor at a top-notch university making mediocre contributions to this top-notch community


Jun
15
revised How many expected people needed until 3 share a birthday?
deleted 37 characters in body
Jun
15
revised How many expected people needed until 3 share a birthday?
added 1161 characters in body
Jun
14
asked How many expected people needed until 3 share a birthday?
Jun
14
comment Second pair of matching birthdays
I have worked (unsuccessfully) at finding a closed form for the constant $c \approx 1.88$ that you approximate via your python program above. Unfortunately the integral that so nicely turns into $\sqrt{\pi/2}$ ends up being much harder with the ${n \choose 2}$ multiplier.
Jun
14
accepted A seeming paradox in a coin-flipping game
Jun
13
answered Why is it that, $\forall x \in \mathbb{Z},\ x^5 \equiv x \pmod{10}$?
Jun
10
comment Prove that if $n$ is a composite and $p \gt \sqrt[3]n$, then $n/p$ is a prime.
If you look at the edit history, it used to say "composite" at the time my response was offered.
Jun
4
accepted Second pair of matching birthdays
Jun
1
comment Second pair of matching birthdays
Very nice! I have been working on this problem since I posted it and I followed virtually the exact same steps as you do above, but you are faster. I just last night wrote the same program you did (in C instead of Python, but they're almost identical!). I feel guilty seeing all the work you did on this... I'm doing this just for fun (it's summer after all!). Cheers.
Jun
1
comment Second pair of matching birthdays
Well, I mostly understand what you did, but you approximated the median (tosses needed to get a 50% probability) rather than the mean, and they are not asymptotically equal for this problem (as you point out). Based on computer simulations I've run, your 55% estimate isn't quite right: for small $M$ we need about 60% more, and for larger $M$ (say 100,000) it's less than 50%. I don't think this 2-collision mean is proportional to $\sqrt{M}$ like the 1-collision mean is.
Jun
1
revised Second pair of matching birthdays
deleted 4 characters in body
May
31
revised Second pair of matching birthdays
added 499 characters in body
May
31
comment Second pair of matching birthdays
I agree with you that this is the probability of obtaining 2 (or more) collisions throwing $n$ balls into $M$ bins, but I was asking for an expectation. Every technique I know of requires computing a sum.
May
31
comment Second pair of matching birthdays
My statement is "ball lands in an occupied bin" twice; that would encompass both or your scenarios. (Restricting to either of your two sub-cases would be interesting problems as well... I would be happy to see a solution to any of them.)
May
31
asked Second pair of matching birthdays
May
26
revised Expected tail and head length of $\rho$ for a finite random function
deleted 11 characters in body
May
18
awarded  Nice Answer
Apr
28
answered Pythagorean theorem and its cause
Apr
24
comment Expected length of a sequence that contains all words of a given length.
I know I'm getting old when a related question was asked by me and I have no memory of asking it.
Apr
24
asked Expected length of a sequence that contains all words of a given length.