Let Y 1 Y 2 Y n denote the order statistics of a random sample of size n from a distribution that has pdf f(x) 3x 2 3 , 0 x , zero elsewhere (a) Show that P(c Y n 1) 1 c 3n , where 0 c 1 (b) If n is 4 and if the observed value of Y 4 is 2 3, what is a 95 confidence interval for

Question: Let Y 1 < Y 2 < < Y n denote the order statistics of a random sample of size n from

Let Y₁ < Y₂ < · · · < Y_n denote the order statistics of a random sample of size n from a distribution that has pdf f(x) = 3x² θ³, 0 < x < θ, zero elsewhere.
(a) Show that P(c < Y_n/θ < 1) = 1 − c³ⁿ, where 0 < c < 1.
(b) If n is 4 and if the observed value of Y₄ is 2.3, what is a 95% confidence interval for θ?

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