All Questions
Tagged with birthday expected-value
17
questions
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:
...
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 ...
- 77
0
votes
2
answers
243
views
The Facebook Birthday Problem（Birthday Problem Variation） [closed]
The Facebook Birthday Problem:
This problem stems from the classic Birthday Paradox.
It says:
How many friends do you need for the probability of having at least one friend with a birthday each day ...
- 19
0
votes
2
answers
74
views
Expected number of days which are birthdays for k people - confused by linearity intuition
I understand this has been asked before but I still cannot understand the intuition behind it. A lot of the answers I've seen seem to just state that it's due to linearity of expectation and that it ...
- 37
5
votes
1
answer
200
views
Birthday paradox - variance, parallelisation, simple proofs?
I am looking for an elementary proof of the fact that expected time for finding a colision with $n$ bins is $\sqrt{\frac{\pi n}{2}} + O(1)$. The proof that I knows relies on the asymptotic expansion ...
- 2,889
1
vote
2
answers
998
views
Expected number of aces in a poker hand
So I'm having difficulty understanding a certain idea. Say I have a standard $52$ card deck (fairly shuffled, etc.) and I pull $5$ cards from it. We ask, what is the expected value of the number of ...
- 13
-3
votes
2
answers
223
views
Birthday Problem: Expected number of people in a room [closed]
If an infinite amount of people enter a room one by one, what is the expected number of people in the room when you first find two that share the same birthday?
(Assuming no leap years and every ...
- 31
2
votes
0
answers
251
views
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 ...
- 2,677
0
votes
1
answer
719
views
Expected number of triples of friends
There are $n$ people are at a party. The probability that each pair of people is friends is $\frac{1}{2}$ (independent). Let $X$ be the number of triples of people that are friends. Find $E[X]$
For ...
1
vote
2
answers
61
views
Expected value vs probability
Sorry in advance, it is probably a stupid question.
I encountered it when I was thinking about the birthday problem. The probability of having at least one pair of the same birthday is
$$ 1- \frac{365\...
- 21
1
vote
2
answers
405
views
Combinatorics problem related to Birthday Problem from Introduction to Probability
Problem
A group of 50 people are comparing their birthdays (as usual, assume their birthdays
are independent, are not February 29, etc.). Find the expected number of days in the year on which at ...
- 229
1
vote
0
answers
104
views
Generalized birthday paradox, expected number of birthday days
Suppose we have m objects and we draw one uniformly n times with replacement. Some objects will be drawn at least once, some never. What is the expected value of the number of objects that are drawn, ...
- 235
2
votes
1
answer
631
views
Birthday problem with $110$ people - need help fixing my approach to get the variance
Let $X$ be the number of distinct birthdays in a group of $110$ people (i.e., the
number of days in a year such that at least one person in the group has that birthday). Under the usual assumptions (...
- 1,715
1
vote
1
answer
127
views
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 ...
- 119
1
vote
1
answer
83
views
Expected number of slots required for channel access - Birthday paradox
Let $n$ be the number of users who want to access a channel divided into with $s$ time-slots and let $n<<s$.
Each user randomly chooses one time-slot (out of $s$) for accessing the channel.
A ...
- 305