Expected number of hash collisions

Question

I feel like I\'m way overthinking this problem, but here goes anyway...

I have a hash table with M slots in its internal array. I need to insert N elements into the

Answer 1

The formula for the SUM(x*(x+1)/2) metric can be found here, and the expected value appears to be (n/2m)* (n+2m -1).

Don't know about the variance, IANAM.

Answer 2

You'll find the answer here: Quora.com. The expected number of collisions for m buckets and n inserts is

n - m * (1 - ((m-1)/m)^n).