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Suppose Y, Erponential (B) for i-1,...,Tn (a) Obtain the MLE, MOME and MVUE of B. (b) Obtain the MLE and MVUE of B2. (c) Obtain a level α > 0 most powerful (MP) test for Ho : β-1 vs. Ha : β-2...
If X ~ N(0, σ2), then Y function of Y is X follows a half-normal distribution; i.e., the probability density This population level model might arise, for example, if X measures some type of zero-mean difference (e.g., predicted outcome from actual outcome) and we are interested in absolute differences. Suppose that Yi, ½, ,y, is an iid sample from fy(ylơ2) (a) Derive the uniformly most powerful (UMP) level α test of 2 2 0 versus Identify all critical values associated...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...
2. Perform the following .05 level test: Ho: 6 = 2.5 vs. Ha: 0 < 2.5, given a random sample of 10 pieces of data had a mean of 13.6 and a standard deviation of 1.7. Ho: Test Statistic: Ha: p-value: Conclusion (Circle Answer): Fail to Reject Ho R eject Ho
n be a random sample from a Gamma distribution with (a) Show there exists a uniformly most powerful test for testing Ho vs H. Show that the critical region can be expressed as an inequality for Y-:-1X, that is it will have the form [Y>cor the form Y < c]. Explain which one of the two and why (b) Is there a uniformly most powerful test for testing Ho : θ 1 vs H1 : θメ1? axqplai n be a...
Problem 5 (15pts). Suppose that we observe a random sample X. from the density Xn 1 0 2 0, else, where m is a known constant which is greater than zero, and 0>0. (a) Find the most powerful test for testing Ho : θ Bo against b) Indicate how you would find the power of the most powerful test when θ-e-Do not perform (c) Is the resulting test uniformly most powerful for testing Ho :0-00 against Ha :e> et Explain...
2. Suppose we observe the pairs (X, Y), i-1, , n and fit the simple linear regression (SLR) model Consider the test H0 : β,-0 vs. Ha : Aメ0. (a) What is the full model? Write the appropriate matrices Y and X. (b) What is the full model SSE? (c) What is the reduced model? Write the appropriate matrix XR. (d) What is the reduced model SSE? (e) Simplify the F statistics of the ANOVA test of Ho B10 vs....
1. Suppose that Y ∼ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U = cY. (b) Identify the distribution of U as a standard distribution. Be sure to identify any parameter values. (c) Can you find the distribution of U using MGF method also? I. Suppose that Y ~ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U cY. (b) Identify the distribution of U...
Y = C + I + G + NX (1) C = α + β(1 − t)Y (α > 0; 0 < β < 1) (2) I = θ − δi (θ > 0; δ > 0) (3) G = g + T (g > 0) (4) NX = (X − M) (5) Using differential calculus: solve for the change in national GDP(Y) with respects to a change in government expenditure(g)
Suppose a test of H0: μ = 0 vs. Ha: μ ≠ 0 is run with α = 0.05 and the P-value of the test is 0.052. Using the same data, a confidence interval for μ is also constructed. (a) Of the following, which is the largest confidence level for which the confidence interval will not contain 0? 90% 94% 95% 96% 99% (b) Of the following, which is the smallest confidence level for which the confidence interval will contain...
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0, 0<y<1 elsewhere Find the most powerful test with significance level a=0.05 to test: HO: 0=1 vs. Ha: 0=2.