situation. Suppose X1,..., Xn d N(μ₁, σ²) and Y₁, . 22d ~ , Xm 2 N(μ2, 02) are all independent, and we'd like to test Ho M1 = μ2. Let A(0; D) denote the likelihood ratio-here, evaluated on the set o D= {X1, Xn, Y₁,..., Ym}. = {(μ1, M2) μ1 = M2} 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(0; D) = (n+m) log 1+ nm(XY)²] (n+m)S² where X Ŷ = Y₁ + ··· + Ym n m n m and S² = Σ(X; – X)² + Σ(¥¿ − Ÿ)². = [(X;- i=1 j=1 [Hint: You can use the fact that, given a set of numbers {1,..., zn} and their average z = identity ±1(zi — a)² = Σ²²±1(²i − z)² + n(z − a)² holds for any a. - (21++zn)/n, the
situation. Suppose X1,..., Xn d N(μ₁, σ²) and Y₁, . 22d ~ , Xm 2 N(μ2, 02) are all independent, and we'd like to test Ho M1 = μ2. Let A(0; D) denote the likelihood ratio-here, evaluated on the set o D= {X1, Xn, Y₁,..., Ym}. = {(μ1, M2) μ1 = M2} 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(0; D) = (n+m) log 1+ nm(XY)²] (n+m)S² where X Ŷ = Y₁ + ··· + Ym n m n m and S² = Σ(X; – X)² + Σ(¥¿ − Ÿ)². = [(X;- i=1 j=1 [Hint: You can use the fact that, given a set of numbers {1,..., zn} and their average z = identity ±1(zi — a)² = Σ²²±1(²i − z)² + n(z − 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
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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 to get the final equation.
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