Statistical Inference

1. [27 marks] A preliminary test of a possible carcinogenic compound can be performed by measuring the mutation rate of microorganisms exposed to the compound. An experimenter places the compound in n = 24 petri dishes and records the following number of mutant colonies (X1, X2, ..., X24): 6, 5, 5, 3, 1, 1, 2, 3, 5, 2, 5, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 5, 3, 1 The number Xm' = 1,2, , . . . , 24 of mutant colonies is believed to follow a Poisson distribution (PA(X,- = cc) = f(.r,/\\) = 63,\i) [3 marks] Suggest a simple unbiased estimator W of the parameter h(/\\) = AeA = P(X1 = 1) (i.e., the probability that exactly one colony will emerge)