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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
Solve for b please
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
Solved in 6 steps with 20 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill