a. Explanation Let Y 1 , Y 2 , ... , Y n is a random sample from the probability density function given as follows: f ( y ) = { 3 y 2 θ 3 ; 0 ≤ y ≤ θ , 0 ; Elsewhere . The distribution function of y is obtained as follows: F ( y ) = ∫ f ( y ) d y = ∫ 3 y 2 θ 3 d y = 3 θ 3 ∫ y 2 d y = 3 θ 3 ( y 3 3 ) = y 3 θ 3 The probability density function of n t h order statistic ( Y ( n ) ) is given and obtained as follows: b. To determine Obtain an MVUE of θ .

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Question

Chapter 9.5, Problem 63E

To determine

Prove that the probability density function of Y(n) is as follows:

f(n)(y)={3ny3n−1θ3n ; 0≤y≤θ,0 ; Elsewhere..

To determine

Obtain an MVUE of θ.

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Chapter 9.5, Problem 62E

Chapter 9.5, Problem 64E

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Chapter 9 Solutions

Mathematical Statistics with Applications

Ch. 9.2 - Prob. 1E Ch. 9.2 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample from the...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.2 - Suppose that Y1, Y2, , Yn is a random sample from...Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.3 - Applet Exercise How was Figure 9.1 obtained?...Ch. 9.3 - Applet Exercise Refer to Exercise 9.9. Scroll down...

Knowledge Booster

Prove that the probability density function of Y ( n ) is as follows: f ( n ) ( y ) = { 3 n y 3 n − 1 θ 3 n ; 0 ≤ y ≤ θ , 0 ; Elsewhere . .

Solution Summary: The author proves that the probability density function of Y_n is as follows:

Prove that the probability density function of Y(n) is as follows:

f(n)(y)={3ny3n−1θ3n ; 0≤y≤θ,0 ; Elsewhere..

Obtain an MVUE of θ.

Want to see the full answer?

Chapter 9 Solutions

Prove that the probability density function of Y ( n ) is as follows: f ( n ) ( y ) = { 3 n y 3 n − 1 θ 3 n ; 0 ≤ y ≤ θ , 0 ; Elsewhere . .

Solution Summary: The author proves that the probability density function of Y_n is as follows:

Prove that the probability density function of Y(n) is as follows: f(n)(y)={3ny3n−1θ3n ; 0≤y≤θ,0 ; Elsewhere..

Obtain an MVUE of θ.

Want to see the full answer?

Chapter 9 Solutions

Prove that the probability density function of Y(n) is as follows:

f(n)(y)={3ny3n−1θ3n ; 0≤y≤θ,0 ; Elsewhere..