Type B (2pts for each problem) Suppose that X = (X,...,Xn) is a random sample drawn...

 

 

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Type B (2pts for each problem) Suppose that X = (X₁,...,Xn) is a random sample drawn from the normal distribution with mean R and variance o² > 0. Let X = 1 Xi/n and Sn = (X-X)²/(n-1). 1. If the parameter space are = {(μ₁0): |μ| = 1,0 >0}, prove that (Xn, Sn) would not be complete and sufficient for (,0) 0. 2. Give an example of ancillary statistic for (μ, σ). 3. Show that (Xn, Sn) is independent of your ancillary statistic. 4. Let 0₁ = P((Y-μ)2 < 1), where Y is an unobservable random variable with the same N(μ, o2) as X₁,..., Xn. Show that the UMVUE of 01 is where V = (X₁ X2)²/S². 2 P(V≤2), 5. Find the UMVUE of 02₂ = μ/√². Type B (2pts for each problem) Suppose that X = (X₁,...,Xn) is a random sample drawn from the normal distribution with mean R and variance o² > 0. Let X = 1 Xi/n and Sn = (X-X)²/(n-1). 1. If the parameter space are = {(μ₁0): |μ| = 1,0 >0}, prove that (Xn, Sn) would not be complete and sufficient for (,0) 0. 2. Give an example of ancillary statistic for (μ, σ). 3. Show that (Xn, Sn) is independent of your ancillary statistic. 4. Let 0₁ = P((Y-μ)2 < 1), where Y is an unobservable random variable with the same N(μ, o2) as X₁,..., Xn. Show that the UMVUE of 01 is where V = (X₁ X2)²/S². 2 P(V≤2), 5. Find the UMVUE of 02₂ = μ/√².

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1 If the parameter space are uo pl 10 0 prove that Xn Sn would not be c... View the full answer