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5. Consider the following sample of size 11 from U(0 - 1, 0 + 1) is given by -0.71, 0.3, -0.4, -0.63, -0.81, -0.7, 0.1, -0.01, 0.02, -0.96, -0.92. Find the MLE of 0. [4] 6. Determine the MSE of a = X which is used to estimate the mean of a N(, o') distribution based on a random sample of n observations. (3] 7. The capacities (in ampere-hours) of 10 batteries were recorded as follows: 140, 136, 150, 144, 148, 152, 138, 141, 143, 151. (a) Compute a 95 percent of two-sided confidence interval for o2. (b) Compute a value & that enables us to state, with 99 percent confidence, that o is less than v. [3+2] 8. The annual rainfall in centimeters at a certain weather station over the last ten years has been as follows: 17.2 28.1 25.3 26.2 30.7 19.2 23.4 27.5 29.5 31.6. Scientists at the weather station wish to test whether the average annual rainfall has increased from its former long term value 22 cm. Test this hypothesis at the 5% level, stating any assumptions that you make. [4]