I am trying to solve the following problem.
Let there be $n$ urns and let us have $k$ balls. Assume we put every ball into one of the urns with uniform probability. Denote by $X_i$ the random variable counting the number of balls in urn $i$. If $X = min\{X_1,\ldots,X_n\}$, what is $E[X]$?
As a more general question, one could ask: what is the expected value of the minimum of some equally distributed random variables?
I do not see any way of solving it besides using the definition of expected value which results in a nasty expression.
I believe there is some better technique for approaching this kinds of problems.
Anyone happens to know how?