5,608 reputation
52040
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location California
age
visits member for 3 years, 6 months
seen Aug 12 at 15:56

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


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.
Apr
21
comment Prove or disprove isomorphic graphs
It should be classified as "group theory" instead of "graph theory." Even if this problem came from graph theory, your presentation of it leaves no trace of that evolution and you've given it as a pure group theory problem.
Apr
21
answered Prove or disprove isomorphic graphs
Apr
10
answered Classifying Algebraic Structures as Fields
Mar
25
comment Explain to me what these symbols mean.
The confusion often arises from the fact that many writers call $dy/dx$ a "symbol" as if it were atomic, but then later start doing algebra with it. This leads to the question, "well, then what is $dy$ really?"