Page 263, 4.4.8.* Let Y₁ < Y₂ < Y3 < Y4 < Y5 denote the order statistics of a random sample of size 5 from a distribution having pdf f(x) = 2e-²x, 0 < x <∞, zero elsewhere. Show that Z₁ = Y4 and Z₂ = Y5 - Y4 are independent.
Page 263, 4.4.8.* Let Y₁ < Y₂ < Y3 < Y4 < Y5 denote the order statistics of a random sample of size 5 from a distribution having pdf f(x) = 2e-²x, 0 < x <∞, zero elsewhere. Show that Z₁ = Y4 and Z₂ = Y5 - Y4 are independent.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Page 263, 4.4.8
Transcribed Image Text:**Order Statistics and Exponential Distribution**
**Exercise 4.4.8**
Let \( Y_1 < Y_2 < Y_3 < Y_4 < Y_5 \) denote the order statistics of a random sample of size 5 from a distribution having probability density function (pdf) \( f(x) = 2e^{-2x}, \) for \( 0 < x < \infty, \) and zero elsewhere.
Show that \( Z_1 = Y_4 \) and \( Z_2 = Y_5 - Y_4 \) are independent.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON