Mixing
Using Poisson to calculate the probability of total number of goals scored in a certain number of matches
1
$begingroup$
I know I can use the Poisson distribution to calculate the probability of x goals being scored in a match, based on the average number of goals scored per game in that particular league.
However, how do I calculate the probability of, for example, at least 31 goals scored in total across 8 matches in the same league, assuming I know the average number of goals scored per match in that league is 3.3?
Thanks.
poisson-distribution
edited Feb 2 at 10:01
Bernard
124k741117
asked Feb 2 at 8:03
CPMCPM
63
$endgroup$
|
show 1 more comment
1
$begingroup$
I know I can use the Poisson distribution to calculate the probability of x goals being scored in a match, based on the average number of goals scored per game in that particular league.
However, how do I calculate the probability of, for example, at least 31 goals scored in total across 8 matches in the same league, assuming I know the average number of goals scored per match in that league is 3.3?
Thanks.
poisson-distribution
edited Feb 2 at 10:01
Bernard
124k741117
asked Feb 2 at 8:03
CPMCPM
63
$endgroup$
1
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
1
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28
|
show 1 more comment
1
1
1
1
$begingroup$
I know I can use the Poisson distribution to calculate the probability of x goals being scored in a match, based on the average number of goals scored per game in that particular league.
However, how do I calculate the probability of, for example, at least 31 goals scored in total across 8 matches in the same league, assuming I know the average number of goals scored per match in that league is 3.3?
Thanks.
poisson-distribution
edited Feb 2 at 10:01
Bernard
124k741117
asked Feb 2 at 8:03
CPMCPM
63
$endgroup$
I know I can use the Poisson distribution to calculate the probability of x goals being scored in a match, based on the average number of goals scored per game in that particular league.
However, how do I calculate the probability of, for example, at least 31 goals scored in total across 8 matches in the same league, assuming I know the average number of goals scored per match in that league is 3.3?
Thanks.
poisson-distribution
poisson-distribution
edited Feb 2 at 10:01
Bernard
124k741117
asked Feb 2 at 8:03
CPMCPM
63
edited Feb 2 at 10:01
Bernard
124k741117
asked Feb 2 at 8:03
CPMCPM
63
edited Feb 2 at 10:01
Bernard
124k741117
edited Feb 2 at 10:01
Bernard
124k741117
edited Feb 2 at 10:01
Bernard
124k741117
124k741117
asked Feb 2 at 8:03
CPMCPM
63
asked Feb 2 at 8:03
CPMCPM
63
asked Feb 2 at 8:03
CPMCPM
63
63
1
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
1
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28
|
show 1 more comment
1
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
1
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28
1
1
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
1
1
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28
|
show 1 more comment
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1
$begingroup$
The expected number of goals is $lambda=8cdot3.3=26.4$, The formula for Poisson distribution is $e^{-lambda}frac{lambda^k}{k!}$.
$endgroup$
– robjohn♦
Feb 2 at 8:29
$begingroup$
Thanks. What is k?
$endgroup$
– CPM
Feb 3 at 9:06
$begingroup$
It might be useful to read a bit about the Poisson Distribution.
$endgroup$
– robjohn♦
Feb 3 at 12:29
$begingroup$
Yes sorry, pretty obvious really. Thanks for your help.
$endgroup$
– CPM
Feb 3 at 20:00
1
$begingroup$
To take this on another step, how do I calculate the probability of at least 50 goals being scored across two leagues with different averages of goals per game? For example, league 1 averages 3.3 goals per game, 8 games to be played, λ = 26.4. League 2 averages 2.2 goals per game, 10 games to be played, λ = 22. I assume it's not as simple as using the Poisson of the sum of the expected number of goals from the two leagues, i.e. 48.4?
$endgroup$
– CPM
Feb 4 at 13:28