Let $\displaystyle X$ 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 $\displaystyle X$.
b) What is the likelihood ratio test of the null hypothesis vs the alternative hypothesis at the level $\displaystyle \alpha = 0.2 $and$\displaystyle \alpha = 0.5$?