0
votes
0answers
72 views

balls in bins — waiting time until $k$ bins are occupied

Consider the classic balls in bins problem: we throw balls one by one into $n$ bins independently and uniformly. Define $\tau(k)$ for $1 \le k \le n$ to be the number of balls we have thrown until $k$ ...
0
votes
3answers
60 views

Count all events for k distinguishable items in n distinguishable bins

I want to count all the possible cases that I can distribute k distinguishable items in n distinguishable bins, for example for 3 items and 2 bins I have the next n^k the possible cases are: I ...
1
vote
2answers
110 views

Urn problem: replacing white balls with black once selected

I'm trying to find the probability of an outcome where, using the traditional example, white balls are replaced by black balls once selected. Initially I have $n$ white balls and $\mu$ samples. I ...
10
votes
1answer
335 views

Hyper Birthday Paradox?

There are $N$ buckets. Each second we add one new ball to a random bucket - so at $t=k$, there are a total of $k$ balls collectively in the buckets. At $t=1$, we expect that at least one bucket ...