Talk:Birthday problem/Archive 1

message: I'm very surprised with the very last paragraph of the article.  I have mathematical education, so I'm not a "non-mathematician".  I don't know about logarithms in English tradition, but in Russian `ln' stands for natural logarithm only, `lg' stands for base 10 logarithm and `log' can be a general logarithm with arbitrary base (the base is specified as index; if it is missed then the base typically doesn't matter for instance in expressions like O(log n)).
I think it would be just to remove the reference to "non-mathemations" as offensive.  I accept that `log' can mean natural logarithm in English tradition, but I think its fair to take into account that for some (mathematically educated) people it is exactly `ln' that stands for natural logarithm.
::Paul Pogonyshev
:I agree and have amended accordingly.  Please feel free comment and/or revert. -- ALoan (Talk) 09:57, 16 Jul 2004 (UTC)
replies: text: Since it's not part of the Halmos quote I won't be militant about it.  If the Halmos quote had gone on a bit longer one would have seen him using "log" to mean natural log.  Nowadays both "ln" and "log" are commonly understood by mathematicians to mean natural log.  When Halmos wrote his autobiography, only about 20 years ago, he expressed contempt for the practice of many non-mathematicians of using "ln" rather than "log" for natural log, and said no mathematician had ever done that.  By 1984, the date of publication, his claim was exaggerated.  Nonetheless, it is still not unusual today to find mathematicians using "log" for natural log.  Michael Hardy 19:59, 16 Jul 2004 (UTC)
thread_title:  Notations for logarithms 

message: Does anyone know how to derive a direct solution to the birthday paradox(i.e. the way it is done on the article, the probability that it is not true is derived; then, that is subracted from one; I want to see a method to get the probability of a match without solving for the other one first).  I know that the article's method is correct, but would be intrigued by the alternative solution because I attempted(and failed) to solve it that way.  If someone knew it, I'd appreciate it if they posted it in the article. Superm401 04:58, 15 Jan 2005 (UTC)
replies: text: This method of switching to the complement is really a pretty and quite powerful trick; it's next to impossible to solve the problem without it. You'd have to distinguish between and deal separately with numerous cases: exactly one matching pair, exactly two matching pairs, exactly three matching pairs, ..., exactly one matching triple, exactly two matching triples,..., one matching quadruple,..., exactly one matching pair and one matching triple, ... etc. (and each of those cases is harder than the single case you have to solve when you switch to the complement). In the end, you'd have to do superhuman algebra to simplify your huge sum down to our tiny little formula. AxelBoldt 03:50, 26 Apr 2005 (UTC)
thread_title:  Direct Solution 

message: The article states the for a number of 366 or more people, the probability is 100%. But what if someone was born in Feb 29th in a leap year?
Should this need a correction? Plus, how should the probability for n=366 be affected because of the probability of 1 or more people be born on a leap year?
:The article makes it clear that a year is assumed to have 365 days, plus other variables (distribution of birth dates through the year, incidence of twins and other multiple births, etc) are ignored. -- ALoan (Talk) 10:47, 17 Feb 2005 (UTC)
replies: text:  Perhaps a section on the complexities introduced by considering leap year would be informative. Actually in a school setting (where students tend to be born in a narrow range relative to the 4-year leap year cycle) you would need to take into acount the demographics of the population.  While this would make the problem too messy to solve in any clean way, it would illustrate the fragile nature of a closed form solution. -- Jake 01:22, 18 October 2005 (UTC)
thread_title:  Leap Years 

message: I've already stated that I don't think Halmos's quotation should remain in full. I don't see any reason that this particular article should discuss pedagogy in this level of generality where most of our mathematics articles do not. Dmharvey  Talk 13:21, 3 October 2005 (UTC)
replies: text: I think that Halmos' quote is doing two things at once. I agree that Halmos is talking about pedagogy, and to that extent it is out of place, here. But at the same time he is also explaining how his argument helps to provide a fuller understanding of the birthday problem, and I think this latter point is wholly relevant here. I don't really see how we can get rid of the former and keep the latter. Perhaps It might be better to remove this quote to a note at the bottom. I will be bold and do this, and see what folks think. Feel free to revert if anybody doesn't like it. Paul August ☎ 16:08, 3 October 2005 (UTC)

text: As far as I'm concerned, the pedagogic part should go. The aspects that are not irrelevant are inappropriate. If we want to attribute the mathematical argument above to Halmos - fine, but I wouldn't spend more than one sentence (or perhaps just a mention of the name) on that. As I said, I'll give it a go. Putting a footnote may be the right direction, thanks Paul.--PizzaMargherita 17:52, 3 October 2005 (UTC)

text: The footnote seems to be a good compromise if some people insist on keeping the quotation. Personally I am not bothered by how the article reads now. - Gauge 03:48, 6 October 2005 (UTC)
thread_title:  On the merits or otherwise of including Halmos's quotation 

message: Using generic d seems unnecessary clutter here, so I do object to that.
:Let's see: "d" = 1 character, "365" = 3 characters. Where's the clutter again?--PizzaMargherita 09:55, 6 October 2005 (UTC)
replies: text: Wait, I may understand what you mean: you don't like p(n;d), you'd rather see p(n). I agree on that part, it's awkward to carry it around, and it's evident from the formula that d is a parameter. I propose we define it as p(n;d) the first time around and we explicitly say that in what follows it's understood that by p(n) we mean p(n;d). This is notwithstanding the proposal below, to give the 365-specific solution at the very top of the article.--PizzaMargherita 09:55, 6 October 2005 (UTC)

text: The introduction has been that way for some time now... you mean the introduction of the article, right? In that case, I can see where you are coming from, as I agree that we shouldn't scare people away. We could give the first formula for 365 and right after state the more general result and carry on with d. What do you think? I'm sure those interested won't have a lot of trouble substituting d with 365... not any more than understanding Taylor series truncations or the probability of complementary events. And the importance and applications of this problem have nothing to do with birthdays. That's why I think that general d-results will be more useful to people who land here.--PizzaMargherita 12:24, 6 October 2005 (UTC)

text: Indeed! Paul August ☎ 03:54, 8 October 2005 (UTC)
thread_title:  Generic ''d''-formulae vs. specific 365-formulae 

message: Is the table in Near matches really correct? It doesn't match with my calculated
probabilities for near matches, nor my empirical tests. Also, unless I'm doing something
seriously wrong, one is not required to use the inclusion/exclusion principle
to calculate this.
For k=5, 8 ppl are required (59.3158%), k=6, 7 ppl (55.0188%), k=7, 7 ppl (60.6174%).
--Yarin 20:43, 6 August 2005 (UTC)
replies: text: Could somebody give the details of these calculations to evaluate? --Neshatian 12:12, 9 May 2006 (UTC)
thread_title:  Near mathches 

message: The link in the merge template on the page refers here, but I don't think anyone has actually started to talk about it yet.  I don't think that page should be merged.  I'm doubtful about whether it should even be kept.  It uses obscure abbreviations, doesn't explain itself, and the table may be a copyvio.  Furthermore, I don't think the idea of a birthday distribution is nearly as common as the "paradox" itself.  I'd like to remove the merge tag.  What do others think? Superm401 | Talk 17:26, July 16, 2005 (UTC)
:It looks like a copyvio of http://www.mathcad.com/library/LibraryContent/puzzles/soln28/exact28.html --Audiovideo 14:19, 19 July 2005 (UTC)
thread_title:  Merge 

message: I have a couple of problems with the "Reverse Problem" section, but I'm not too sure how to fix them.
# I think there is a little notation inconsistency, in that p and n are both functions and variables. I don't know how to put it, but I have the feeling that in the same sentence p is both a given point and a function.
# Two problems are stated, but one solution is given. I think it would be nicer to state only one problem, and perhaps mention that it's a quantile kind of problem. By the way, in my [Mood, Graybill, Boes] the quantile is defined in a completely different way than in the WP article.
::The q-th quantile of a random variable X or of the corresponding distribution is defined as  the smallest number ξ that satisfies FX(ξ) <= q.
::I guess this is a comment for that other page...--PizzaMargherita 20:27, 3 October 2005 (UTC)
thread_title:  Reverse problem 

message: I just removed two links from the article:
* http://www.teamten.com/lawrence/puzzles/birthday_paradox.html (almost no content)
* http://science.howstuffworks.com/question261.htm (full of ads; not very meaningful, too)
feel free to flame me, if you think that was a bad idea --J.N. 15:48, 24 October 2005 (UTC)
thread_title:  links removed 

message: :"it becomes relevant that due to the way hospitals work, more children are born on Mondays and Tuesdays than on weekends."
Er, really? Do hospitals suppress labor if it occurs on the weekend? -VJ 08:11, 5 January 2006 (UTC)
replies: text: I took this to mean that labor is more often induced near the beginning of the week, for some reason. --RCS talk 05:40, 18 January 2006 (UTC)

text: Here are some German links: http://www.welt.de/data/2005/09/30/782511.html http://www.kinderwelten.de/cgi-bin/websql?sqlid=18349&nid=1019 They say the reason is e.g. that Caesarean sections become more popular. --NeoUrfahraner 10:24, 19 January 2006 (UTC)

text: Here is a better one in English with data from Enland and Wales: http://www.statistics.gov.uk/downloads/theme_health/HSQ9book_V1.pdf There is an obvious seven day cycle, with fewer births on Sundays compared with births on other days of the week. The average number of births on a Sunday during 1979 was 1,373, with a standard deviation of 60, whereas the overall daily average in 1979 was 1,748, with a standard deviation of 211. (Page 7). --NeoUrfahraner 11:24, 19 January 2006 (UTC)
thread_title:  birthday distribution 

message: This article could address another very common curiosity:  the expected range of birthday matches for certain group sizes.  To phrase it another way:  present a table showing group size X and the expected collision range N to M, where the odds are even that at least N and at most M birthdates will recur among those X people.  Alternately, a link to a "birthday paradox calculator" applet including this feature (among others) would be similarly useful (this is different from the current link to a Mac-OS birthday grapher application). -- Mike 17:15, 11 January 2006 (UTC)
thread_title:  Suggestion for another table 

message: A while back User:205.170.235.246 changed the empirical test so that the increment would be performed after all operations, rather than before. I reverted the edit, on the grounds that: revert with reluctance: I that the increment operator is supposed to before the logic. It's a bit weird, I agree. In this edit, the anon has done it again.
So, I hacked out a quick test using PHP this way:
// append ?alt to URL to use anon's method
$days = 365;
$numPeople = 1;
$prob = 0.0;
while ($prob < .5) {
    if (!isset($_GET['alt'])) $numPeople++;
    $prob = 1 - (1-$prob) * (1-($numPeople-1) / $days);
    echo "Number of people: $numPeople";
    echo "Prob. of same birthday: $prob";
    if (isset($_GET['alt'])) $numPeople++;
}
and I determined that whether or not the increment was present didn't make a difference in the final result. However, when it was at the back (anon's method), a probability when there was 1 person was given (obviously 0).
The reason, however, why this is weird, is because in most cases, the increment is indeed performed after the loop, as this for statement illustrates:
$days = 365;
$prob = 0.0;
for ($numPeople = 1; $prob < .5; $numPeople++) {
    $prob = 1 - (1-$prob) * (1-($numPeople-1) / $days);
    echo "Number of people: $numPeople";
    echo "Prob. of same birthday: $prob";
}
We can also alleviate the aforementioned concerns by beginning the loop with $numPeople = 2, starting with the first "logical" case.
In the end, I am more for a solution that uses for rather than while. Any comments? — Ambush Commander(Talk) 22:19, 27 January 2006 (UTC)
replies: text: I'm with you.  I would change it to a for. Superm401 - Talk 01:44, 28 January 2006 (UTC)
replies: text: Changed. — Ambush Commander(Talk) 20:37, 28 January 2006 (UTC)
thread_title:  Increment numPeople before or after 

message: Whose common intuition does it contraddict? I asked my mother and my sister, neither of whom is particularly good at maths, wheter in their opinion it is more likely that in a 23-people group all birthday are different or at least two are equal. Both of them answered the latter. In addition, nobody on buying 23 trading cards of a set of 365 would expect them to be all different. --Army1987 21:04, 8 February 2006 (UTC)
replies: text: Likely the way you phrased the question. Although we should find a survey. — Ambush Commander(Talk) 21:29, 8 February 2006 (UTC)
thread_title:  Whose common intuition? 

message: Hmm... is it linkspam? — Ambush Commander(Talk) 20:42, 11 February 2006 (UTC)
thread_title:  OS X program 

message: The Birthday_paradox#Binomial_distribution calculation is not valid at all. While it somehow approximates the real probability, it lacks the necessary rationality:
1. The paradox is talking about "at least two persons may have same birthday". This includes not only pairs, but also 3 persons groups, 4 persons groups and 23 persons as well. This calculation is just considering pairs. The cumulative distribution of B(X,253,1/265) equals 1 in X=253 while forgetting all other n-groups.
2. The binomial distribution is just valid for independent events. These 253 possible pairs are not independent. For example for people A, B, C, ... having same birthday for pair (A,B) and (B,C) means having same day for (A,C). For instance Pr(X=252) should equals Pr(X=253) in this context while formula doesn't so. --Neshatian 11:50, 3 April 2006 (UTC)
replies: text: Thanks to Michael Hardy, the section was removed. --Neshatian 15:05, 23 April 2006 (UTC)
thread_title:  Mistake in binomial distribution 

message: According to this worfram site (which cites a US census table - wish I could find the origional source) birthday frequencies are actually skewed to the months of July, August and September (in that order). It makes sense intuitivly because those months are roughly 9 months behind the winter holidays (more time spent indoors, cheerful festive atmosphere etc.) Extremely interesting article though, I enjoyed it alot --Cinexero 13:30, 15 June 2006 (UTC)
thread_title:  Corrected Note 1 

message: Can't you just divide a year in 52 weeks (52.17 or whatever) and use the same approach you do with 365 days?  —Preceding unsigned comment added by 193.198.81.100 (talk) 21:31, 28 April 2009 (UTC)
thread_title:  "Near matches" why so much trouble? 

message: "23"! --nlitement [talk] 13:37, 30 September 2006 (UTC)
thread_title:  Mystery! 

message: This was useful to me testing a password generation programme, and I couldn't find anywhere else in Wikipedia that gave this information.  The hash collision article could perhaps link directly to this section.
I suggest that the section's usefulness would be improved by the addition that for 1 << n << d, as is typical, the formula reduces to n^2/2d.
Also, knowing the standard deviation would be useful, as I'd like to assess how reasonable my observed number of collisions is. Jlittlenz 05:07, 8 December 2006 (UTC)
thread_title:  Collision counting 

message: Is there any reason for the notion that the "birthday problem" is computing p given n, while the "reverse birthday problem" is computing n given p (as implied in #Reverse problem)? Insofar as the two are separate problems, it seems to me that the ordinary birthday problem is computing the minimal n such that p > ½, so the "reverse birthday problem" would be computing p given n. —RuakhTALK 16:23, 8 December 2006 (UTC)
thread_title:  Forward vs. reverse? 

message: In the article, it claims, although it cannot actually be 100% unless there are at least 366 people.[1] However, the real number should be 367, because there are 366 days in a leap year. Someone could be born on February 29th, and then no one would have the same birthday out of 366 people. Correct me if I'm wrong, Thanks, RAmen, Demosthenes 21:48, 15 February 2007 (UTC)
replies: text: Yes, you are correct, but check the footnote. We're assuming 365 days in a year for sake of simplicity in calculations. — Edward Z. Yang(Talk) 22:48, 15 February 2007 (UTC)
thread_title:  366 People isn't necessarily 100% 

message: I think this is an interesting subject, great article i think it's featured article quality comments?  I dont know how to tag it for that status myself.. —The preceding unsigned comment was added by 83.49.105.6 (talk) 20:56, 12 March 2007 (UTC)
replies: text: There are instructions at WP:FAC. Greeves (talk • contribs) 15:50, 31 March 2007 (UTC)
thread_title:  Featured Article 

message: Paradox? Don't you mean conundrum. a paradox is something I thought to be impossible!! And this is not. —The preceding unsigned comment was added by 131.111.8.98 (talk • contribs).
:To quote the third sentence of the article:
::This is not a paradox in the sense of leading to a logical contradiction; it is called a paradox because mathematical truth contradicts naive intuition: most people estimate that the chance is much lower than 50%.
:—RuakhTALK 01:49, 18 April 2007 (UTC)
replies: text: Look up "paradox" in a dictionary.  The first definition usually is something like, "A true statment that seems not to make sense at first glance."  Then, somewhere further down the list of definitions, you'll find the one that says, "a mathematical proposition that can neither be proven, nor disproven."  —Preceding unsigned comment added by 192.55.12.36 (talk) 20:08, 29 February 2008 (UTC)
thread_title:  Conundrum, not paradox 

message: I wish to take issue with the statement, "After having met people with n different birthdays (n < 365), the chance that the next person you meet has a colliding birthday is (365-n)/365."
Suppose I am just getting started.  I have met one person, and recorded their birthday.  The number of different birthdays n is then 1.
The quoted text asserts that there are 364 chances out of 365 that the second person I meet will have the same birthday as the first one.  This seems counter-intuitive.  Likewise, if my list of birthdates is long, and I have n = 364, then the equation predicts that there is only one chance in 365 that the next person I meet has a birthday that is already on my list.
In summary, the equation says that at the beginning when n is small, I will have a large number of collisions, and as the size of my list of birthdays grows, the   likelihood of a collision will decrease.  --Jamesglong 18:14, 13 August 2007 (UTC)
replies: text: Heh, good catch. I'm not sure how to fix this, though; in general, that section is assuming some things I'm not sure about. I think for now I'll label it "disputed", and we can work on fixing it up. —RuakhTALK 18:49, 13 August 2007 (UTC)

text: I think that (365-n)/365 is the probability that the next person you meet will have a non-colliding birthday. After you've collected one birthday, there is a good chance (364 in 365) that the next person will have a different birthday. Once you've collected 365 birthdays, you cannot collect any new birthdays and the probability is zero.--143.215.153.96 19:53, 14 August 2007 (UTC)
thread_title:  365 different birthdays -- what am I missing? 

message: The pigeon hole principle says that there MUST be at least two people with the same birthdays if you have 367 or more people. Imagine 366 people (allowing for leap years), with one birthday on each of the 366 days of the (leap) year. When you introduce the 367th. person, this persons birthday can only happen on one of the already occupied birthdays.  —Preceding unsigned comment added by 80.2.196.26 (talk) 18:22, 14 September 2007 (UTC)
replies: text: Please read the first footnote. :-) —RuakhTALK 21:43, 14 September 2007 (UTC)
thread_title:  [[Pigeonhole principle]] 

message: I think one of the earlier posts discussing a test with groups of 50 may have been looking for the same birthday date (month/day/year) as opposed to simply the same day (month/day).  Can you compute the odds for the same date?  I suppose the distribution of people would impact the odds - but, can you make estimates based on assumptions for your groups ("even distribution of ages 20-60", or "distribution mirroring earth's population at each age")?  Now that seems like a fun excercise.  And one I'm not capable of completing.  :-(
69.134.204.75 20:58, 14 September 2007 (UTC)
replies: text: Well, the "even distribution of ages 20–60" version is not hard: it's the same as the normal birthday problem, but assuming 14,975 distinct days instead of 365. With that assumption, it would take 145 people before you have a 50% chance that two had the same DOB — still amazingly few, IMHO. The latter version would obviously requiring knowing that distribution, which I do not. (And the math would be significantly more complicated, too. I'm actually not sure exactly how one could go about that, other than a brute-force or probabilistic method.) —RuakhTALK 21:53, 14 September 2007 (UTC)
thread_title:  How about sharing the same birthday date? 

message: This article does not meet the Good Article criteria at this time, and will not be listed. Currently, I'd probably grade it as somewhere on the border of Start-class and B-class. The main issues are some major organizational and prose issues, as well as insufficient reference citations. I am also unclear whether the items mentioned under 'references' were really used to back up anything in the article at all, or are, in fact, just extra books that some might want to use to look up additional information about the subject. In which case, the section should be renamed to further reading.
There's a considerable amount of text in the 'notes' section. Why isn't this used in the article itself. These are clearly not footnotes! It would help editors to review WP:CITE for guidelines on how to properly use inline citations to cite material in an article.
The section header titles are fairly long, and not very clear and concise. It would be advisable to shorten and simplify these so that they are easier to understand when reading the table of contents. Some sections might be reorganized and merged with others as well, and check that all second, third, and fourth level subsection headers are absolutely necessary.
Many sections seem overly dependent on some very complex equations with very little text to actually describe the significance and meaning of these equations. This is likely to scare off many readers. Equations should also have a citation, so that we can verify that what is being included is clearly not original research. The citation should not appear next to the equation itself, it should appear in the sentence preceding and referring to the equation, usually immediately after a colon, such as in "the probability that two birthdays coincide can be attributed to the following equation:your citation
The lead section actually does a reasonably good job of introducing the topic, but could better summarize the article. It might help to review WP:LEAD for tips on this. Also, the 'birthday attack' is mentioned in the lead, and briefly in the text, but there is no source for this information, and the text is pretty vague.
Hopefully, this will help editors improve the article. Good luck! Dr. Cash 04:59, 2 October 2007 (UTC)
replies: text: footnote86.42.66.94 (talk) 00:59, 10 January 2008 (UTC)

text: Thanks! :-) —RuakhTALK 14:50, 2 October 2007 (UTC)
thread_title:  GA Review