Linked Questions
14 questions linked to/from birthday problem - expected number of collisions
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Probability that N people have the same birthday [duplicate]
This question is from the book "Heard on the Street."
There are N = 25 people at a party. One person asks everybody to announce their birthdays and for anyone who has the same birthday as ...
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Birthday Problem: Expected Number of people with common birthday [duplicate]
This might be a different variant of the typical birthday problem. Given a room of $n$ people, let $N$ be a random variable representing the number of people who have a birthday common with at least ...
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Probability question (Birthday problem)
I was wondering if someone could critique my argument here. The problem is to find the probability where exactly 2 people in a room full of 23 people share the same birthday.
My argument is that ...
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Birthday problem - expected number of shared birthdays
Given $m$ people and an $n$ possible "days of the year", what is the expected number of days which 2 or more people share as a birthday (if the distribution of birthdays is iid uniform over ...
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birthday problem - which solution for expected value of collisions is correct?
I am trying to understand the difference of the two solutions for the expected value of collisions for the birthday problem:
https://math.stackexchange.com/a/35798/254705 derives the following ...
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Figuring out the variance of the birthday paradox
Update to reflect what I think is the calculation for $E[X_1\cdot X_2]$
Given n people, if I want to estimate how many of them are likely to have an overlapping birthday with any other person, how do ...
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Extension of the Birthday Problem
How do you find the expected number of people (or the expected number of pairs) among the n that share their birthday within r days of each other?
For the regular birthday problem, it's $n\left(1-(1-...
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Mean number of unique choices given n people choosing randomly from a set of N elements
My question is similar to the birthday problem, but I can't seem to find a simple solution. The question (in a general form) is that, given a set of $n$ people who each choose elements from a set of $...
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Expected value of birthday problem (combination)
Suppose that a child desires $10$ different toys for her birthday.
Twenty people will come to her birthday party, each of them equally likely to bring any one of the $10$ toys.
Let $X$ be the ...
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Why is $(1 - \frac{1}{p})^n$ close to $e^{-\frac{n}{p}}$ when $n$ and $p$ are large?
Looking at this answer by Henry birthday problem - expected number of collisions and struggling to figure out why it matches this other formula provided to me on a programming related question. Thanks!...
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If people sharing the same birthday raise their hand, how many hands do you expect to see raised?
The following question is taken from an interview book assuming that no calculator is provided.
Question: There are $25$ people at a party. One person asks everybody to annouycne their birthday, ...
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Variation of Birthday problem - Group of n people
I know this has been posted several times and I have gone through most of the relevant posts.
Here is one which I am having a difficult time to solve:
There are 450 people in a room; (1) how many of ...
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Expected value of the number of days where k people share their birthdays
I am trying to find the expected value of the number of days where exactly $k$ people have a birthday in a class which consists of $60$ independently chosen people.
For $k = 0, 1, 2, 3, 4$
I am ...
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Number of date collisions in birthday problem
If I generate uniform random integers from 1 to K and count how many unique numbers I get $n_\mathrm{unique}$, I empirically obtain:
the mean is: $\frac{2K}{\pi}$
the variance is $\frac{K}{\pi^{2}}$.
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