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$?