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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.

Bernard
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CPM
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    The expected number of goals is $\lambda=8\cdot3.3=26.4$, The formula for Poisson distribution is $e^{-\lambda}\frac{\lambda^k}{k!}$. – robjohn Feb 02 '19 at 08:29
  • Thanks. What is k? – CPM Feb 03 '19 at 09:06
  • It might be useful to read a bit about the Poisson Distribution. – robjohn Feb 03 '19 at 12:29
  • Yes sorry, pretty obvious really. Thanks for your help. – CPM Feb 03 '19 at 20:00
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    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?

     – CPM Feb 04 '19 at 13:28
  • I think that two different leagues are independent so I guess given the fact that you already know the prob of X goals for league 1 and Y goals for league 2, you can find all the combinations of X+Y >=50 and then sumproduct the corresponding probs. – Fierce82 Mar 06 '19 at 10:21

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