How do I change a poisson spreadsheet into a bivariate version?

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To convert a Poisson spreadsheet into a bivariate version, one must consider whether the two variables are independent or dependent. If independent, the Poisson distributions can be multiplied; however, if they are dependent, correlation information is necessary. A key restriction involves incorporating draw probability as a parameter, where the draw probability is calculated as the sum of the products of the two distributions. The user has noted that their current calculations yield a draw probability lower than the actual, indicating that additional factors, particularly draw probability, must be integrated into the Poisson distribution. To accurately modify the distribution, it is essential to account for these draw probabilities in the calculations.
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I have an excel spreadsheet that uses poisson to figure out the probability of correct scores in soccer matches.

How do I amend the spreadsheet to use a bivariate poisson distribution?
 
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If the two variables are independent, just multiply the Poisson distributions of each. If they are not independent, what information about the correlation do you have?
 
HallsofIvy said:
If the two variables are independent, just multiply the Poisson distributions of each. If they are not independent, what information about the correlation do you have?

1. There is additional restriction - draw probability as parameter for distribution. Draw - this is the case when M(t) = N(t).
In common Pdraw = sum(M(ti)*N(ti)), i = 0, 1, 2 ...

2. I have tried to multiply the Poisson distributions of each for calculation the spreadsheet, but calculated Pdraw is lower than fact Pdraw. And calculated data don't correlate with fact data. Results from this that I don't take into account some factors (first of all, draw probability), which shall correct Poisson distribution.

How I can take into account draw probability to modificate the Poisson distribution?
 
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