Question: 1. [28 marks] Suppose a sample X = (X1, X2, . .., Xn) from the density f(I, 0) = (1+ 0)1, r E (0, 1),

1. [28 marks] Suppose a sample X = (X1, X2, . .., Xn) from the density f(I, 0) = (1+ 0)1, r E (0, 1), 0 elsewhere is given where 0 > -1 is the unknown parameter. a) Find a minimal sufficient statistic T for 8. Give reasons for your answer. b) Calculate the Fisher information about o contained in the statistic T that you found in a). Show that it is equal to (1+0 ) . c) Find the MLE of 0 and also the MLE of h(0) = 146. d) Find the Cramer-Rao lower bound for the variance of an unbiased esti- mator of h(0) = 140

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