Problem 5. The following table counts the number of outcomes in 100 trials for each of four events. Roll A B C D Count 27 24 12 37 Assume the outcomes at event AD independently follow a Poisson distribution with parameters AA, A3, A0 and AD. We want to test the null hypothesis that AA = AB+AQ Use the parameterization AA = A , AB = A0 and A0 = Ml). (1) Use Maximum Likelihood Estimation to estimate the value A which is the expected value of the number of outcomes in A or the total number of outcomes in B and C when the null hypothesis that these expectations are the same is true. (2) Estimate Ac under the condition that is imposed by the null hypothesis. Use your answer from part (a) and use an MLE. (3) Calculate the x2 test statistics and determine if it is statistically signicant at an 0: = 0.05 level