Answer all

ii 2 U {20'} 3. For the. matrix A = 2 3 1 l 2 1 a.) Find all eigenvalues of the matrix. h.) Find all eigenvactors of the matrix. a.) is the matrix diagonaiizabla'.' If at}! state a matrix 1.\" and a diagonal matrix D for which 1312113 = D. 4. Suppose that n light bulbs are burning simultaneously to determine the lengths of their lives. We shall assume that they burn independently and that the lifetime of each bulb has the exponential distribution with parameter . Let X2- denote the lifetime (in thousand hours) of bulb i, for 2' : 1, . . . ,n. The pdfJ mean and variance of exponential distribution Expw) are 1 1 1%) = fie'93, 1300 = -, Var(X) = 2- 3 X3 (a) What does the central limit theorem say about the distribution of W when n is large? (b) Find a two-sided 95% condence interval of the mean lifetime (1/3). Express your answer in terms of n, X and z (the 2 critical values). Interpret the condence interval you obtain in context of the situation. (c) Now, suppose that we want to test whether or not the mean lifetime is 1000 hours, we would consider H0:,8=1Ha:71. Derive the likelihood ratio statistic. (d) Denote the likelihood ratio statistic by A(X). Should the null hypothesis H0 be rejected when A(X) is large or small? (0) What is the large-sample distribution of 2 log AU?) when the null hypothesis H0 is true? (f) Explain what a Type I error would mean in context of this problem. 6. (Submit a screenshot of your written or typed answer.) The fitness trainer wants to learn more about exercise habits of MATH 1P98 students. You will report your findings on the mean number of days that all MATH 1P98 students exercise for more than 20 minutes and whether it differs between females and males. Based on the results you have obtained from Questions 4 and 5, prepare a brief (no more than 34 of a single-spaced page, Times New Roman font size 12) report. This report should include three headings and should include any findings you think are noteworthy: Introduction (statement of problem, sample size, survey details, context, etc.), Results (report, summarize, and interpret the results of the confidence interval and hypothesis test), and Conclusions/Recommendations (inference on the population, limitations of study, recommendations to improve future study, etc.).rou Hand Fa20 Fa20 Micro Mod Class G funct B Biost Micro Sign HI X cture.com/courses/1295643/quizzes/1439355?module_item_id=10338094 ct) - ger.. R RStudio Question 20 1.2 / 1.2 pts The equilibrium constant K for the synthesis of ammonia is 6.8x10' at 298 K. What will K be for the reaction at 375 K? N2(g) + 3H2(g) = 2NH3(g) AH = -92.22 kJ/mol 6.75 x 105 1.42 x 109 6.85 x 105 O 326