Could you please answer question h)

75% ST2002 Assignment 3 2022 Question 1 A company operates a drinking water purifying process at two different sites and there is interest in examining the purity of the water produced. Data have been collected from each site over n weeks. The data are denoted by C. y). .... (X.)). where x and y, denote a measurement of purity, on a scale between 0 and 1, at sites 1 and 2 respectively, in week/ An appropriate probability model is given by the density function f(x,y) = B8XP-16-1 where 0 1. The two parameters and determine the marginal distributions of purity at sites 1 and 2 respectively. If Band 8 are equal the purity in each site is the same. The joint likelihood function for 8 and 8 is: d) Use H to calculate a Wald 95% Confidence Interval for 6-8 and provide an interpretation of the interval. e) Calculate the maximised log-likelihood under H. 1) Calculate the maximised log-likelihood under Ho g) Calculate the number of restrictions for this test. h) Derive the rejection region based on the chi-square distribution (set the significance level a to be 0.05). 1) Make a conclusion as to whether or not there is evidence of a significant difference in the purity of the water produced at the two sites. L(8,8) a [ ] 66x4+xdur = 8484 *14741) The joint log-likelihood function is 48,5) = nloge + niloge (8) + (8 - 1)Eloge (x) + (8 - 1) Llog,00) Your task is to test the following hypotheses of interest: Ho: B = 8 H: 88 You are asked to do this by 1) calculating a 95% Confidence interval for 8-8 and it) by carrying out a Generalised Likelihood Ratio Test (GLRT). a) Derive the maximum likelihood estimators for Band 8. b) Given that n = 30.2 loge(x) = -1.79 and loge) = -1.63, evaluate the maximum likelihood estimates of 8 and 8 c) Calculate the Hessian matrix H and show that al 0 882 H= 021 021 Labas 282 Rain coming AC. de 2024 21/04/2022