situation. Suppose X1,..., Xn ~ N(μ1,02) and Y₁,..., Xm d N(μ2, σ²) are all independent, and we'd like to test Ho μ1 =μ2. Let A(0; D) denote the likelihood ratio-here, evaluated on the set o D= {X1, Xn, Y₁, ..., Ym}. = {(μ1, μ2) μ₁ = μ2} CR2 and for (a) Briefly state the answers to the following questions: (i) What are the MLES of μ1, M2, σ² under the current model assumption? (ii) What are the MLES of μ1, M2, 02 while being restricted to the set no? (b) Show that 2 log A(No; D) = (n + m) log [1 + nm(X-Y)²] (n+m)S² where + Xn Y₁₁ + ...+Ym X n m n m , and_S² = Σ(X; – X)² + Σ(Ÿ¿ − Ÿ)². i=1 j=1 [Hint: You can use the fact that, given a set of numbers {1,..., zn} and their average z = identity (-a)² = ²²±1(i − )² + n(ž− a)² holds for any a.] - (21+ +zn)/n, the
situation. Suppose X1,..., Xn ~ N(μ1,02) and Y₁,..., Xm d N(μ2, σ²) are all independent, and we'd like to test Ho μ1 =μ2. Let A(0; D) denote the likelihood ratio-here, evaluated on the set o D= {X1, Xn, Y₁, ..., Ym}. = {(μ1, μ2) μ₁ = μ2} CR2 and for (a) Briefly state the answers to the following questions: (i) What are the MLES of μ1, M2, σ² under the current model assumption? (ii) What are the MLES of μ1, M2, 02 while being restricted to the set no? (b) Show that 2 log A(No; D) = (n + m) log [1 + nm(X-Y)²] (n+m)S² where + Xn Y₁₁ + ...+Ym X n m n m , and_S² = Σ(X; – X)² + Σ(Ÿ¿ − Ÿ)². i=1 j=1 [Hint: You can use the fact that, given a set of numbers {1,..., zn} and their average z = identity (-a)² = ²²±1(i − )² + n(ž− a)² holds for any a.] - (21+ +zn)/n, the
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Solve for b please
![iid
~
N(μ2,02) are all independent, and we'd like to test
iid
situation. Suppose X1, ..., Xn
~
N(μ1,02) and Y₁,..., Xm
Ho:
M1 =μ2.
Let A(0; D) denote the likelihood ratio-here, evaluated on the set o
D = {X1, … … …, Xn, Y₁, . . ., Ym }.
=
{(M1, M2) μ1
:
=
2} CR2 and for
(a) Briefly state the answers to the following questions: (i) What are the MLEs of μ1, μ2, σ² under the current
model assumption? (ii) What are the MLES of μ1, #2, σ² while being restricted to the set no?
(b) Show that
2 log A(No; D) = (n + m) log |1+
nm(XY)²]
(n+m)S²
where
X1+
+ Xn
Y₁ +
+ Ym
Y
n
M
n
m
and S² = Σ(X; – Ñ)² + Σ(Ÿ¿ − Ÿ)².
= (x −
+
i=1
[Hint: You can use the fact that, given a set of numbers {1,..., Zn} and their average z
(z - a)² = Σ² ²±1 (zi — ž)² + n(ž − a)² holds for any a.
identity
=
(21+
+ Zn)/n, the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2F93da3219-f336-4c6d-9bab-45cc9158444d%2F4q6u0sa_processed.png&w=3840&q=75)
Transcribed Image Text:iid
~
N(μ2,02) are all independent, and we'd like to test
iid
situation. Suppose X1, ..., Xn
~
N(μ1,02) and Y₁,..., Xm
Ho:
M1 =μ2.
Let A(0; D) denote the likelihood ratio-here, evaluated on the set o
D = {X1, … … …, Xn, Y₁, . . ., Ym }.
=
{(M1, M2) μ1
:
=
2} CR2 and for
(a) Briefly state the answers to the following questions: (i) What are the MLEs of μ1, μ2, σ² under the current
model assumption? (ii) What are the MLES of μ1, #2, σ² while being restricted to the set no?
(b) Show that
2 log A(No; D) = (n + m) log |1+
nm(XY)²]
(n+m)S²
where
X1+
+ Xn
Y₁ +
+ Ym
Y
n
M
n
m
and S² = Σ(X; – Ñ)² + Σ(Ÿ¿ − Ÿ)².
= (x −
+
i=1
[Hint: You can use the fact that, given a set of numbers {1,..., Zn} and their average z
(z - a)² = Σ² ²±1 (zi — ž)² + n(ž − a)² holds for any a.
identity
=
(21+
+ Zn)/n, the
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information.
VIEWStep 2: Compute the MLEs of μ1, μ2, σ² under the current model assumptions.
VIEWStep 3: Compute the MLEs of μ1, μ2, σ² while being restricted to the set Ω_0.
VIEWStep 4: Prove the given equation using the given identity.
VIEWStep 5: Substitute the likelihood ratios in the above equation.
VIEWSolution
VIEWStep by step
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