Let (XaU ,Xapy , a be a random sample of size N from A p( x,2 ) (a) Find the maximum likelihood estimator of jl when S is known (b) Find the maximum likelihood estimator of 2 when jl is known Is it unbiased Table 9 2 Farm X X X 123 75 15 156 145 4 175 5682 6 0 2 5 60 0 5 24 3 0 5 70 5 2 0 6 179 8 1 5 7 165 14 4 0 8 134 13 4 0 9 137 7 1 5 10 175 19 1 5 11 135 13 0 5 12 175 12 2 5 13 240 7 2 0 14 175 27 4 0 15 197 16 6 0 16 125 6 5 0 17 227 13 5 0 18 172 13 11 0 19 170 34 2 0 20 172 19 6 5

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Question: Let = (XaU...,Xapy , a = be a random sample of size N from A/p(|x,2 ). (a) Find the maximum likelihood estimator of |jl when

Let = (XaU...,Xapy , a = be a random sample of size N from A/p(|x,2 ).

(a) Find the maximum likelihood estimator of |jl when S is known.

(b) Find the maximum likelihood estimator of 2 when |jl is known. Is it unbiased?

Table 9.2 Farm X X X 123 75 15 156 145 4

Table 9.2 Farm X X X 123 75 15 156 145 4 175 5682 6.0 2.5 60 0.5 24 3.0 5 70 5 2.0 6 179 8 1.5 7 165 14 4.0 8 134 13 4.0 9 137 7 1.5 10 175 19 1.5 11 135 13 0.5 12 175 12 2.5 13 240 7 2.0 14 175 27 4.0 15 197 16 6.0 16 125 6 5.0 17 227 13 5.0 18 172 13 11.0 19 170 34 2.0 20 172 19 6.5

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