The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. The Chi-squared distribution gives us a number beyond which we reject fairness. However, there is another possibility. If the difference between the fair model and the observed frequency is too small, that is also suspicious. The scientist G. Mendel was accused of faking the data by R. A. Fisher because the results were too good to be true. We also explore the "Lucky Sum", which is also a part of the Pick 4. We determine which sum is most likely to occur, and what the odds of winning are if you play the sum most likely to occur.
Zhou, Xiaona, "Validation of a Lottery" (2018). CUNY Academic Works.