5. We have two independent samples of n observations X1, X2, .. . , Xn and...
5. We have two independent samples of n observations X1, X2,... , Xn and Yi, Y2,..., Y, We want to test the hypothesis Ho : μ®-,ty versus the alternative H, : μ*-t ,ty. (a) First, assume that the null hypothesis Ho is true and find the MLE for μ-Ae-μΥ. (b) Then plug this estimate into the log likelihood along with the MLE's μΧ-x and My to calculate the LRT statistic. (c) Is this likelihood ratio test equivalent to the test...
5. We have two independent samples of n observations X1,X2-…Xn and Yi,½, . …Ý, We want to test the hypothesis H0 : μ®-ty versus the alternative H1 : μζ μυ. (a) First, assume that the null hypothesis H0 is true and find the MLE for μ- - y. (b) Then plug this estimate into the log likelihood along with the MLBs μτ-x and μ to calculate the LRT statistic. (c) Is this likelihood ratio test equivalent to the test that...
5. we have two independent samples of n observations X1,X2, ,x, and Yi, ½, ,y, We want to test the hypothesis Ho M Hy versus the alternative Hi: Hr y (a) First, assume that the null hypothesis Ho is true and find the MLE for μ Ha-μυ (b) Then plug this estimate into the log likelihood along with the MLE's μ--x and μυ-D to calculate the LRT statistic (c) Is this likelihood ratio test equivalent to the test that rejects...
Thank you so much! 5. We have two independent samples of n observations X1,Xy,.. . ,x, and Y. Ya, . … We want to test the hypothesis Ho : μ,-μυ versus the alternative Hi : μ, μν. (a) First, assume that the null hypothesis Ho is true and find the MLE for μ (b) Then plug this estimate into the log likelihood along with the MLE μ'.. and 1,-j) to calculate the LRT statistic. (e) Is this likelihood ratio test...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...
2. Suppose that we have n independent observations x1, ,Tn from a normal distribution with mean μ and variance σ2, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 7-2 log max L(μ, σ*) )-2 log ( max L(u, i) μισ (c) Explain as clearly as you can what happens to T, when our estimate of σ2 is less than 1. (d) Show...
4. (30 points) Suppose that we have two independent random samples: X1, X2, ..,,Xn are exponential (9) and Y.Y2, ,,Yn are exponential(A) (aside: be happy l didn't make it(!) a. Find the likelihood ratio test of Ho: θ 1 versus H1 : θ . b. Show that the test in part a. can be based on the statistic ΣΑΜ c. Find the distribution of T when Ho is true.
Please justify each step! 4. (30 points) Suppose that we have two independent random samples: X1, X2, ...,, Xn are exponential(8) and Y. Y, , , Yn are exponential(A) (aside: be happy I didn't make it 〈!) a. Find the likelihood ratio test of Ho: θ μ versus H1:0 # . b. Show that the test in part a. can be based on the statistic c. Find the distribution of T when Ho is true. 4. (30 points) Suppose that...
3. Suppose that we have two independent random samples: X1, Xn are exponential(), and Y1,... . Ym are μ. You do not need to find the critical value of exponential(μ). Find the LRT of H0 : θ the test. μ versus Ha : θ