We have n observations xi that are i. i. d. from a Normal distribution with mean-0...
We have n observations that are i. i. d. from a Normal distribution with mean 0 anod unknown variance. We want to test using a Generalized Likelihood Ratio Test. Calculate the test statistic T for the GLRT. You can assume that the MLE for the variance is Tn 62 2
1, we have n observations xi that are i. i. d. from a Normal distribution with mean= 0 and unknown variance. We want to test using a Generalized Likelihood Ratio Test. Calculate the test statistic T for the GLRT. You can assume that the MLE for the variance is Tt 2 -1
1. We have n observations xi that are і. i. d. from a Normal distribution with mean-0 and unknown variance. We want to test using a Generalized Likelihood Ratio Test. Calculate the test statistic T for the GLRT. You can assume that the MLE for the variance is 2 i-1
1. We have n observations xi that are і. i. d. from a Normal distribution with mean-0 and unknown variance. We want to test using a Generalized Likelihood Ratio Test. Calculate the test statistic T for the GLRT. You can assume that the MLE for the variance is 2 i-1
We have n observations x, that are i. i. d. from a Normal distribution with mean-0 and unknown variance. We want to test using a Generalized Likelihood Ratio Test. Calculate the test statistic T for the GLRT. You can assume that the MLE for the variance is TL 7t
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...
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...
We are looking to calculate the power of a one-sided test from n independent observations xi from a N (µ, σ2 ) distribution with a null hypothesis of H0 : µ = µ0 and an alternative H1 : µ > µ0. Supposing that we know σ2, we can form a test statistic T = (x¯ − µ0)/(σ/√n) and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power...
4. We have n independent observations from a geometric distribution with unknown parameter θ. PoX, k 0(1- 0)1 or1,2,3,... We wish to test the null hypothesis θ-1/2 versus the alternative θ 1 /2. we can show that the MLE θ-1/2. Write out the appropriate LRT statistic as a function of the x, the mean of the observations