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(a) Let fy (y) be the probability density function (pdf) of Y), the k-th order statistic, 1

(a) Let fy (y) be the probability density function (pdf) of Y), the k-th order statistic, 1

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 4CR
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Question 6 Let Y1, Y2,.., Yn be independent uniformly distributed random variables on the in- terval [0, 0]. (a) Let fy (y) be the probability density function (pdf) of Y), the k-th order statistic, 1 < k<n. Show that, for 0<y < 0, n! %3D (k – 1)!(n – k)! On (b) Find E(Y)). (c) Let fyY (Yj, Yk) be the joint pdf of Y) and Yk), where j and k are integers, 1<j<k<n. Show that, for 0 < y; < Yk < 0, n! !! 6-1)(k-3-1)(nーk)1gn+25 (-5)ーナー1(0-2)ース (d) Find E(Y) - Y(k-1)), 2<k <n.
Transcribed Image Text:Question 6 Let Y1, Y2,.., Yn be independent uniformly distributed random variables on the in- terval [0, 0]. (a) Let fy (y) be the probability density function (pdf) of Y), the k-th order statistic, 1 < k<n. Show that, for 0<y < 0, n! %3D (k – 1)!(n – k)! On (b) Find E(Y)). (c) Let fyY (Yj, Yk) be the joint pdf of Y) and Yk), where j and k are integers, 1<j<k<n. Show that, for 0 < y; < Yk < 0, n! !! 6-1)(k-3-1)(nーk)1gn+25 (-5)ーナー1(0-2)ース (d) Find E(Y) - Y(k-1)), 2<k <n.
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