1. determine the likelihood function L(x: 0) = f(x₁,x2,...,xn|0) and the maximum likelihood estimator for
1. determine the likelihood function L(x: 0) = f(x₁,x2,...,xn|0) and the maximum likelihood estimator for
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...
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Please answer number 1
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
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