Mixing
Sequential urn-ball problem: N people, n balls/person, M urns
$begingroup$
Consider $N$ people, each randomly placing $n sim Poisson(lambda)$ balls into $M$ urns (assume no person places multiple balls in the same urn). Urns are then randomly assigned an order in which they will be able to choose one ball. Assume that when an urn's turn arrives, it chooses a ball randomly. When an urn chooses a ball, a match is formed, and the owner of that ball removes all remaining balls from other urns.
I am interested in computing three probabilities:
1) The probability that a person who places exactly $n$ balls in urns forms a match with an urn.
2) The (ex ante) probability that a person forms a match. [That is, the probability that one of their balls is selected by a firm, given that people submit a stochastic number of balls, $n sim Poisson(lambda)$, for some fixed $lambda$.]
3) The (ex ante) probability that an urn forms a match. [That is, the probability of having at least one ball remaining when its turn to pick arrives, given $lambda$.]
probability sequences-and-series combinatorics
asked Jan 28 at 2:14
JohnJohn
255
$endgroup$
add a comment |
$begingroup$
Consider $N$ people, each randomly placing $n sim Poisson(lambda)$ balls into $M$ urns (assume no person places multiple balls in the same urn). Urns are then randomly assigned an order in which they will be able to choose one ball. Assume that when an urn's turn arrives, it chooses a ball randomly. When an urn chooses a ball, a match is formed, and the owner of that ball removes all remaining balls from other urns.
I am interested in computing three probabilities:
1) The probability that a person who places exactly $n$ balls in urns forms a match with an urn.
2) The (ex ante) probability that a person forms a match. [That is, the probability that one of their balls is selected by a firm, given that people submit a stochastic number of balls, $n sim Poisson(lambda)$, for some fixed $lambda$.]
3) The (ex ante) probability that an urn forms a match. [That is, the probability of having at least one ball remaining when its turn to pick arrives, given $lambda$.]
probability sequences-and-series combinatorics
asked Jan 28 at 2:14
JohnJohn
255
$endgroup$
add a comment |
$begingroup$
Consider $N$ people, each randomly placing $n sim Poisson(lambda)$ balls into $M$ urns (assume no person places multiple balls in the same urn). Urns are then randomly assigned an order in which they will be able to choose one ball. Assume that when an urn's turn arrives, it chooses a ball randomly. When an urn chooses a ball, a match is formed, and the owner of that ball removes all remaining balls from other urns.
I am interested in computing three probabilities:
1) The probability that a person who places exactly $n$ balls in urns forms a match with an urn.
2) The (ex ante) probability that a person forms a match. [That is, the probability that one of their balls is selected by a firm, given that people submit a stochastic number of balls, $n sim Poisson(lambda)$, for some fixed $lambda$.]
3) The (ex ante) probability that an urn forms a match. [That is, the probability of having at least one ball remaining when its turn to pick arrives, given $lambda$.]
probability sequences-and-series combinatorics
asked Jan 28 at 2:14
JohnJohn
255
$endgroup$
Consider $N$ people, each randomly placing $n sim Poisson(lambda)$ balls into $M$ urns (assume no person places multiple balls in the same urn). Urns are then randomly assigned an order in which they will be able to choose one ball. Assume that when an urn's turn arrives, it chooses a ball randomly. When an urn chooses a ball, a match is formed, and the owner of that ball removes all remaining balls from other urns.
I am interested in computing three probabilities:
1) The probability that a person who places exactly $n$ balls in urns forms a match with an urn.
2) The (ex ante) probability that a person forms a match. [That is, the probability that one of their balls is selected by a firm, given that people submit a stochastic number of balls, $n sim Poisson(lambda)$, for some fixed $lambda$.]
3) The (ex ante) probability that an urn forms a match. [That is, the probability of having at least one ball remaining when its turn to pick arrives, given $lambda$.]
probability sequences-and-series combinatorics
probability sequences-and-series combinatorics
asked Jan 28 at 2:14
JohnJohn
255
asked Jan 28 at 2:14
JohnJohn
255
asked Jan 28 at 2:14
JohnJohn
255
asked Jan 28 at 2:14
JohnJohn
255
asked Jan 28 at 2:14
JohnJohn
255
255
add a comment |
add a comment |
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