Let \(\displaystyle{X}_{{{1}}},\cdots,{X}_{{{n}}}\) random sample of \(\displaystyle{U}{\left[\theta-{\frac{{{1}}}{{{2}}}};\theta+{\frac{{{1}}}{{{2}}}}\right]}\).Consider

Addison Fuller

Addison Fuller

Answered question

2022-03-22

Let X1,,Xn random sample of U[θ12;θ+12].Consider [X(1); X(n)] a confidence interval for θ. Find their confidence level and show that result is valid for any distribution symmetric around θ

Answer & Explanation

smekkleg5hhp

smekkleg5hhp

Beginner2022-03-23Added 8 answers

Step 1
If X's are i.i.d. and their density is symmetric around θ, then
P(X(1)θ)=P(X(n)θ)=(P(X1θ))n=(12)n.
Thus,
1γ=P(X(1)θ)+P(X(n)θ)=2×(12)n.

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