The questions are the below in a picture. Thank you.

2. 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 A-D independently follow a Pois- son distribution with parameter AA, A3, A0 and AD. We want to test the null hypothesis that AA = A3 + AC. Use the parameterization AA = AAB = A0 and A0 = A(1 6). (a) 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. (b) Estimate AC under the condition that is imposed by the null hypoth esis. Use your answer from part (a) and use an MLE. (0) Calculate the X2 test statistics and determine if it is statistically sig nicant at an a = 0.05 level. ((1) Suppose we change the table to combine the categories B and C. Roll A B or C D Count 27 36 37 Calculate the X2 statistic to test the same null hypothesis that AA and is the same as Aggro