Find the sampling distribution for Y2, the 2nd order statistic for random samples of size n=4 taken without replacement from the finite population consisting of the first 6 positive integers (1,2,3,4,5,6).
Find the sampling distribution for Y2, the 2nd order statistic for random samples of size n=4 taken without replacement from the finite population consisting of the first 6 positive integers (1,2,3,4,5,6).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
Related questions
Question
Expert Solution
Step 1 Introduction
Given that the population consists of the first 6 positive integers (1,2,3,4,5,6), from which we draw samples of size n=4 without replacement.
Thus the total number of ways we can draw these samples of size 4 are .
Y2, the 2nd order statistic for the random sample is nothing but the second smallest number among the 4 numbers.
The possible values Y2 can take are 2,3 and 4. Y2 cannot take values 1 and 6 because:
- if Y2=1, then there needs to be a value less than 1 in the sample, which is not possible
- if Y2=5 or 6 then there are a value less than 1 in the sample, which is not possible
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL