Reference no: EM131669408

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!     q^k(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.