Question: Let \[{{X}_{1}},{{X}_{2}},{{X}_{3}},{{X}_{4}}\] be a random sample from a Poisson distribution with parameter \[\lambda \] and let \[Y={{X}_{1}}+{{X}_{2}}+{{X}_{3}}+{{X}_{4}}\]. You decide to test \[\lambda \] =1.60 versus \[\lambda \] <1.60 using the following decision rule:

Reject \[\lambda \] =1.60 in favor of \[\lambda \] <1.60 when \[Y\le \] 2.

a. Find the type I error, \[\alpha \].

b. Find the type II error , \[\beta \], when \[\lambda \] =1.70.