Assume random sample X1, ..., X, has below distribution: f(x; 0) = 02(x -1)(1 -0)*-2, 0

Assume random sample Xl, ...,Xn has below distribution: f(x; 9) = 92(x - - Also assume the below distribution is the priori distribution for 9: ram + 5) 93 (I 9)2n, ose'l r(2m + Additionally, let (B be the loss from estimating 9 by 9. i) Calculate the posterior distribution of 9 conditional on X, and thus find the Bayes estimator of B, Calculate estimate of 9 if observations were 2, 2, 3, 2, 4, 2, 3. There exists a claim that 9 < 0.4. Test this claim through Bayesian testing with a zero-one loss, using data in ii)