Questions tagged [birthday]
Birthday problems typically look at probabilities and expectations of a random group of individuals sharing birthdays and how this changes as the number of people increase. They often assume that individuals' birthdays are independently uniformly distributed across 365 days but similar problems can use other numbers or assumptions. They can be generalised to wider occupancy and collision problems.
351
questions
3
votes
3
answers
153
views
'deducing' a bound using the first order taylor series. How to make it more precise?
So, I just saw a ‘proof’ that the generalized birthday problem has a median of C*sqrt(n). Though the probability in question is interesting, this question is more about calculus and maybe asymptotics ...
- 2,323
2
votes
1
answer
411
views
Birthday problem with an arbitrary "year" and number of overlapping birthdays
First off, I'm not a mathematician, so if I'm going about this in the wrong way, please let me know.
The problem
I have ~4.1 million timestamps (with second accuracy) when people logged into a ...
- 159k
2
votes
1
answer
52
views
How to modify the birthday formula to account for overlapping sequences?
While calculating the probability that the same sequence of 50 words occurs twice in a file that contains 400 million random words (each word can have 65536 different states, chosen at random)...
...
- 78.3k
2
votes
3
answers
838
views
Birthday probability: Permutation or Combination?
In a class of $30$ people, what is the probability that at least $2$ people share the same birthday?
I would think that I should use $^{365}C_{30}$ for the numerator since order shouldn't matter in ...
- 47.4k
0
votes
1
answer
1k
views
Poisson Distribution Problem relating to birthdays
Consider a random collection of n individuals. When approximating the probability that no 3 of these individuals share the same birthday, a better Poisson approximation than that obtained in the text (...
CommunityBot
- 1
1
vote
1
answer
65
views
Probability problem (maybe linked to birthday paradox)
Good evening. I would like to show the following statement :
Let $n>1$, and $E,F$ two subsets of $[\![ 1,n ]\!]$ randomly and independently chosen such that $|E| = |F| = \lfloor\sqrt{ n }\rfloor + ...
- 825
0
votes
0
answers
25
views
Expected number of collsions in hashing
Suppose we use a hash function h to hash n keys into m slots. Assuming simple uniform hashing, what is the expected number of collisions? (CLRS, 3rd edition, problem 11.2-1)
My solution is as follows:
...
2
votes
1
answer
119
views
What is the limit probability an element of $x \in S$ belongs to $f^n(S)$, for $n \to \infty$?
Let $S$ be a finite set of $|S|=n$ elements and $F$ be the set of all functions $f:S\rightarrow S$.
It's easy to demonstrate that the integer sequence $\{c_i\} = |{\rm Im}(f^i)|$:
is non increasing;
...
- 432
2
votes
2
answers
83
views
Modifying the Birthday Problem Paradox for Arbitrary Situations?
We learned about the birthday problem paradox: If people are in a room with randomly distributed birthdays, very few people are needed for at least two people to have the same birthday.
As I ...
- 159k
2
votes
2
answers
348
views
Probability of birthday chain
Let $B(k,n)$ be the probability that a consecutive birthday chain of length $k$ can be found in $n$ people, excluding leap days and assuming that December 31 and January 1 are consecutive. After some ...
- 688
3
votes
1
answer
149
views
$T$ Pokemon trainers catch a Pokemon every day. How many days does it take until two trainers own Pokemons of the same species?
$T$ Pokemon trainers catch $1$ out of $P$ different species of Pokemons every day.
Every species has the same chance to be caught.
One species can be caught by one trainer multiple times.
In mean ...
- 104k
2
votes
2
answers
96
views
Variation of Birthday problem with n people and exactly t pairs sharing the same birthday
The problem statement is simple: Let there be a group of n people. What is the probability that exactly t pairs will share the same birthday?
All my attempts to solve this problem came down to the ...
- 228
0
votes
0
answers
35
views
Understanding the generalized "Birthday Problem" formula [duplicate]
While practicing frequently asked probability questions during interviews, I came across the classical "Birthday problem". While I understand some of the reasoning explained on wikipedia, ...
- 39
1
vote
2
answers
150
views
What is the probability of someone being born both on a Good Friday that is also Friday the 13th
I was born on April the 13th 1990. The day was also Good Friday. I'm wanting to know what the probability/chances of being born on a Good Friday that is also a Black Friday is/are to have an ...
- 22.6k
13
votes
3
answers
2k
views
Birthday Paradox with Leap Year
I looked online, and found more than one and inconsistent answers to the Birthday Paradox when we throw the leap year into the mix. None of the answers I saw match with my own. I am posting my ...
- 2,792