Question: When a part is selected at random from a particular production batch, there is a probability q that the part is defective. Thus, out of n independently selected parts, the number K of defective units is a random variable with the binomial probability distribution
p[K = k] = n! qk(1 - q)n - k), for k = 0, 1, 2,.....,n
k!(n - k)!
Suppose we receive a shipment of n parts which either came all from production batch 0, with probability of defect q0, or came all from batch 1, with probability of defect q1. Assume that 0
(a) Find the minimum probability of error rule for deciding whether the received units were from batch 0 or batch 1.
(b) Suppose n = 2. Make a labeled sketch of the ROC for the LRT.