Let X have one of the following distributions:


X H_0 H_A
x_1 0.2 0.1
x_2 0.3 0.4
x_3 0.3 0.1
x_4 0.2 0.4


a) Compare the likelihood ratio for each possible value X.
b) What is the likelihood ratio test of the null hypothesis vs the alternative hypothesis at the level \alpha = 0.2 and  \alpha = 0.5?