Let X, and X, be the independent random sample from the following discrete probability mass function: 1 2 3 Px(x;0 = 1) 0.3 0.4 0.2 0.1 Px (x;0 = 2) (a) Find the most powerful test of size a = 0.06...

Extracted text: Let X, and X, be the independent random sample from the following discrete probability mass function: 1 2 3 Px(x;0 = 1) 0.3 0.4 0.2 0.1 Px (x;0 = 2) (a) Find the most powerful test of size a = 0.06 for H, : 0 = 1 versus H : 0 = 2. 0.3 0.1 0.1 0.5 (b) Find the power of the test obtained in (a) (c) When observed values of X, and X, are 1 and 3, respectively, find the MLE of E(X).