5. Bacteria are distributed at random in a uid with mean densityr 9 per unit volume, i.e. lP(no bacteria in volume v) = 89\". A single sample of volume I) is tested by a method which reveals only whether bacteria are present or absent. It is required to decide either 3 = U (decision on) or that 9 > U (decision a1} relative to the cost function 1, lfZOIGZII-lj L(3,a)= 1, if6>0,a:ng, {3, otherwise. (a) Describe the nonstandomized decision procedures and determine which of them are (i) admissible, (ii) unbiased. (b) Suppose the parameter space 9 2 {G1 1}. Identify the risk set for all the nonsrandomized and randomized rules. Determine the minimax decision rule. Is it a randomized rule? (c) Suppose prior weights on 8 = [0,00] are assigned: a discrete weight 7(0)) 2 1 f3 and a continuous density (9) = 283/3, a > 0