Let $\{X_1,\ldots,X_n\}$ be independent identically distributed discrete random variables. I am interested in computing the probability of the event that the sample is duplicate free: $ \mathbb{P}\left( \bigcap_{i
Special case
If $X_k$ are uniformly distributed with the size of the sample space being $d$, this is a classic birthday problem with the answer: $ \mathbb{P}\left( \bigcap_{i
Motivation
Consider IEEE floating point number with mantissa $m$ encoded as $d$-tuple of significant binary digits (i.e. the first bit is always 1), and integer binary exponent $e$. For a random real $0
My approach
Applying inclusion-exclusion principle, the complementary probability is $ \sum_{i
Solutions, ideas, references are welcome.