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(d) Gaussian process: A bachelor project group in the spring of 2022 call themselves the "Gonzos in the Lab" (GL). They have testet different types of concrete, and we have been allowed to use their data for this exam. We will be looking at the pressure strength of A = Leca 300 vs. B Leca 300 with more concrete. We assume that X4, the pressure strength for a random sample of concrete of type A, follows the probability distribution XA similarly for B that XB~ (BOB). 2 (A,A), and {x = i. The first measurements for pressure strength for concrete of type A is: 20.0, x2 = 21.5, x3 = 20.0, = 20.2, 5= 18.4} (N/mm). Usc neutral priors and find posterior distributions for A and TA, and predictive distribution for X4. ii. Draw a confidence curve for TA, and mark an 80% interval estimate ("credible interval") for TA. You get a half score on this assignment if you instead draw the posterior probability distribution (pdf) for TA, and mark the interval estimate in that diagram. iii. The next measurements for concrete of type A are {x6 = 17.3, x7 = 14.9, 28 = 19.4}. Use the previous posterior as your new prior, and find a new and updated posterior probability distribution for A. (You do not need to update TA or X4.) iv. The measurements for pressure strength for concrete of type B is: {y = 25.3, Y2 = 19.7, y3 = 26.1, y = 21.8, y5 = 21.8, y6 = 20.6} (N/mm). Use neutral priors and find the posterior distribution for B. v. Use the last posterior distributions for each , and decide the following hypothesis test with significance a = 0.05: H: PB > PA Th BEST (d) Gaussian process: A bachelor project group in the spring of 2022 call themselves the "Gonzos in the Lab" (GL). They have testet different types of concrete, and we have been allowed to use their data for this exam. We will be looking at the pressure strength of A = Leca 300 vs. B Leca 300 with more concrete. We assume that X4, the pressure strength for a random sample of concrete of type A, follows the probability distribution XA similarly for B that XB~ (BOB). 2 (A,A), and {x = i. The first measurements for pressure strength for concrete of type A is: 20.0, x2 = 21.5, x3 = 20.0, = 20.2, 5= 18.4} (N/mm). Usc neutral priors and find posterior distributions for A and TA, and predictive distribution for X4. ii. Draw a confidence curve for TA, and mark an 80% interval estimate ("credible interval") for TA. You get a half score on this assignment if you instead draw the posterior probability distribution (pdf) for TA, and mark the interval estimate in that diagram. iii. The next measurements for concrete of type A are {x6 = 17.3, x7 = 14.9, 28 = 19.4}. Use the previous posterior as your new prior, and find a new and updated posterior probability distribution for A. (You do not need to update TA or X4.) iv. The measurements for pressure strength for concrete of type B is: {y = 25.3, Y2 = 19.7, y3 = 26.1, y = 21.8, y5 = 21.8, y6 = 20.6} (N/mm). Use neutral priors and find the posterior distribution for B. v. Use the last posterior distributions for each , and decide the following hypothesis test with significance a = 0.05: H: PB > PA Th BEST