If X1, ,Xn are iid with pdf f(x ) e (x )I ,) (x), then Y min X1, ,Xn is sufficient for with pdf fY(y ) ne n(y ) I ,)(y) In Example 9 2 13 a 1 confidence interval for was found using the method of Section 9 2 3 Compare that interval to 1 intervals obtained by likelihood and pivotal methods ...

The confidence interval derived by the method of Section 923 is where y min i x i The ...

If X1,... ,Xn are iid with pdf f(x|) = e-(x-)I[,) (x), then Y = min{X1,... ,Xn} is

Question:

If X1,... ,Xn are iid with pdf f(x|μ) = e-(x-μ)I[μ,∞) (x), then Y = min{X1,... ,Xn} is sufficient for μ with pdf
fY(y|μ) = ne-n(y-μ) I[μ,∞)(y)
In Example 9.2.13 a 1 - α confidence interval for μ was found using the method of Section 9.2.3. Compare that interval to 1 - α intervals obtained by likelihood and pivotal methods.