If X₁, X₂, ..., X is a random sample from the population with E distribution (4,0) with density function : 1 X -x³e ; x > 0 604 f(x|0) =
If X₁, X₂, ..., X is a random sample from the population with E distribution (4,0) with density function : 1 X -x³e ; x > 0 604 f(x|0) =
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
Related questions
Question
Please answer number 3
Transcribed Image Text:If X₁, X₂, ..., Xn is a random sample from the population with Gamma
distribution (4,0) with density function:
1
f(x|0) =
604
To test Ho: 0 = 3 and H₁ : 0 > 3 at the significance level a = 5%
1. determine the likelihood function L(x: 0) = f(x₁,x2,..., Xn0)
and the maximum likelihood estimator for 0
2. determine the ratio of the likelihood function A(x: 00, 0₁) =
L(x: 00)
i
L(x: 0₁)
3. determine the critical region of the test, if known that -
2lnλ(x: 00, 0₁) has a X² distribution
4. give your conclusion about the test based on the following
observations:
1
X₁ 3
2
4
3 4
2
3
x
³e ; x > 0
+3
5
2
LO
6
3
7
3
8
4
9
5
10
3
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 2 steps
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,