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0 votes
1 answer
61 views

Collisions in a Sample [closed]

Based on birthday paradox; Let $d$ be the set of elements randomly chosen from a set of $n$ distinct elements then a) What is expected number of unique elements in $d$ (remaining will be repetition of ...
crypt's user avatar
  • 143
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 ...
Kolja's user avatar
  • 2,889
0 votes
1 answer
221 views

What is the probability of two random elements from two lists are equal? (formal proof)

Suppose $L_1$ and $L_2$ are the lists of random uniform elements with sizes $m$. The elements are from $\{0,1\}^{n}$, e.g. the binary vector in $F_2^n$. What is the probability that $x_1 \in L_1$ and $...
Laura's user avatar
  • 161
0 votes
1 answer
63 views

closed form of multiple in the probability of a two to one collision problem (birthday paradox).

I have a problem where I need to find the chance of finding a collision in a two to one set of size $N$. For example: Let's say I have 10 indices. There are then 5 pairs that map to the same output. ...
Thomas Mc Donald's user avatar