I have an essat to calculate the probability of occurence of a particular number in a lottery. To do this, i will use some statistics and the Poisson distribution and the Poisson distribution.
I assume that i count the appearance of a particular number (for instance, lts say, number 13) per each lottery.
The total number of lotteries increases by one in each lotter (obviously). The number of appearance increases by one in each appearance of number 13 in a lottery.
This means i can calucalate: Total number of appearances of number 13 / total number of lotteries. We will name this λ.
Now, i have to calculate the probability that the number 13 will appear in the next lottery.
For this, i take the Poisson distribution: P=λ^x * e^(-λ)/x!
Here, λ is the previously calculated expression. My question, is what do i put for the x variable?
$x$ would be the number of appearances of $13$ in the next lottery. Why are you using the Poisson distribution? You have observed that the chance of $13$ appearing in a lottery is $\lambda$ in the past, so why not claim that for the probability in the next lottery? The other thing that would make sense to claim would be $\frac {\text{number of numbers chosen}}{\text{number of numbers available}}$ You would expect $\lambda$ to be close to this. You could study whether the past data supports the hypothesis that all numbers are equally likely to be chosen.