Question: (b) Let X1,..., Xn be an i.i.d. sample drawn from the distribution with the probability density function 2x0e-0x2 x 0, f(x) = { 0,

(b) Let X1,..., Xn be an i.i.d. sample drawn from the distribution

(b) Let X1,..., Xn be an i.i.d. sample drawn from the distribution with the probability density function 2x0e-0x2 x 0, f(x) = { 0, otherwise, where 0 is an unknown parameter. i. Find a Method of Moment estimator of 0 by considering EX}. ii. Find the Maximum Likelihood estimator of 0. iii. Discuss how you would like to construct a 90% confidence interval for 0. Also, how would you interpret the meaning of this confidence interval? [Equal weight to each part; 20 marks in total]

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