Questions 2. An experimenter wishes to compare the number of bacteria of types A and B in a water source. A total of n independent water samples are taken from the source, and counts are made for each sample. Let X; denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X1, X2,, X and Y₁, Y2,..., Yn can be considered independent random samples from Poisson distributions with means ₁ and λ2, respectively. n 1. Find the MLE of 7 = 1/(\1 + 2) and show that it is consistent. Solution: 2. Using asymptotic properties of the maximum likelihood estimators and the 8-method find an approximate pivotal quantity and make a 100 ×(1-a)% confidence interval for T. Solution: