Derive a conservative one-sided upper 95 confidence, Ask an Expert

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Assume X~f(x;θ), 0 < θ < 1 where f(x;θ)=(1-θ)θ^(x-1), for x= 1,2,3,4,...
a) Derive a conservative one-sided upper 95% confidence interval for θ if x=4 is observed.
b) Derive a conservative (equal tailed) two-sided 95% confidence interval for θ if x=4 is observed.

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