Remarks for Math 628 Exam I: Mathematical Theory of Statistics, Exams of Mathematical Statistics

Download Remarks for Math 628 Exam I: Mathematical Theory of Statistics and more Exams Mathematical Statistics in PDF only on Docsity! REMARKS FOR SAMPLE PROBLEM SOLUTIONS FOR EXAM I MATH 628 Mathematical Theory of Statistics, 2/14 Beware of the suggestions for solutions. 1. Use the test for variances with χ2(9) because the mean is known. 2. Let L be the likelihood function for the independent random variables and differentiate ln(L) with respect to α to obtain the MLE. 3. K(4) determines the critical region and given the critical region K(2) determines n. 4. Use the result for the difference of two means when the variances are unknown but assumed equal. 5. Let L be the likelihood function so minimize ln(L) to obtain the MLE. 6. n = 93 7. Use the binomial table to determine P (Y < 3|p = .6) where Y is b(4, .6). 8. Use the confidence interval for the difference of two means where the variances are known. 9. Compute P (X̄ > 2.6|µ = 2) and P (X̄ ≤ 2.6|µ = 3). 10. ΣXi. 1