## Hypothesis Testing and Likelihood Function

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 $\alpha = 0.5$?