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math.PR2022
Hitting a prime in 2.43 dice rolls (on average)
Noga Alon, Yaakov Malinovsky
What is the number of rolls of fair 6-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up…
math.PR2022
On Tournaments and Negative Dependence
Yaakov Malinovsky, Yosef Rinott
Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results,…
math.PR2022
On the distribution of winners' scores in a round-robin tournament
Yaakov Malinovsky
In a classical chess round-robin tournament, each of players wins, draws, or loses a game against each of the other players. A win rewards a player with 1 points, a draw…