Mixing
Distribution of successes for k trials among m different groups
$begingroup$
I don't know a better way of titling this, but imagine you've got a sports league with 10 teams. Each year, one team wins the championship. The league has played for 20 years. My question is regarding what best describes the distribution of the average number of championships, treating all the teams as identical.
I can easily calculate the expected number of championships for a specific team (2), as well as the probability that of them winning n championships is $(frac{1}{10})^{n}(frac{9}{10})^{20-n}$.
How then would I calculate probability of any given total distribution compared to expected result of each team winning 2. If, for example, the data for number of championships is {4, 3, 3, 2, 2, 2, 2, 1, 1, 0}, what be be the best way of assessing how unlikely it was that this result occurred?
probability
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
$endgroup$
add a comment |
$begingroup$
I don't know a better way of titling this, but imagine you've got a sports league with 10 teams. Each year, one team wins the championship. The league has played for 20 years. My question is regarding what best describes the distribution of the average number of championships, treating all the teams as identical.
I can easily calculate the expected number of championships for a specific team (2), as well as the probability that of them winning n championships is $(frac{1}{10})^{n}(frac{9}{10})^{20-n}$.
How then would I calculate probability of any given total distribution compared to expected result of each team winning 2. If, for example, the data for number of championships is {4, 3, 3, 2, 2, 2, 2, 1, 1, 0}, what be be the best way of assessing how unlikely it was that this result occurred?
probability
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
$endgroup$
1
$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24
add a comment |
$begingroup$
I don't know a better way of titling this, but imagine you've got a sports league with 10 teams. Each year, one team wins the championship. The league has played for 20 years. My question is regarding what best describes the distribution of the average number of championships, treating all the teams as identical.
I can easily calculate the expected number of championships for a specific team (2), as well as the probability that of them winning n championships is $(frac{1}{10})^{n}(frac{9}{10})^{20-n}$.
How then would I calculate probability of any given total distribution compared to expected result of each team winning 2. If, for example, the data for number of championships is {4, 3, 3, 2, 2, 2, 2, 1, 1, 0}, what be be the best way of assessing how unlikely it was that this result occurred?
probability
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
$endgroup$
I don't know a better way of titling this, but imagine you've got a sports league with 10 teams. Each year, one team wins the championship. The league has played for 20 years. My question is regarding what best describes the distribution of the average number of championships, treating all the teams as identical.
I can easily calculate the expected number of championships for a specific team (2), as well as the probability that of them winning n championships is $(frac{1}{10})^{n}(frac{9}{10})^{20-n}$.
How then would I calculate probability of any given total distribution compared to expected result of each team winning 2. If, for example, the data for number of championships is {4, 3, 3, 2, 2, 2, 2, 1, 1, 0}, what be be the best way of assessing how unlikely it was that this result occurred?
probability
probability
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
asked Jan 18 at 5:18
Leo BloomLeo Bloom
1006
1006
1
$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24
add a comment |
1
$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24
1
1
$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24
$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24
add a comment |
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$begingroup$
This situation is described by the multinomial distribution.
$endgroup$
– littleO
Jan 18 at 5:24