Question: QUESTION 3 [19] Let Y1, Y2, ..., Yn be a random sample from a distribution with probability density function: f ( ) = ed ify

QUESTION 3 [19] Let Y1, Y2, ..., Yn be a random sample from a distribution with probability density function: f ( ) = ed ify > 0 , elsewhere; E(Y) = 20; and V (Y) = 202. (a) What are: (i) the likelihood (L(0) = L(y1, y2, ..., yn10)); and (ii) the log likelihood (In L(0)) of the sample? (6) (b) Use the factorization criterion/theorem to show that Y; is a sufficient statistic for 0. (4) (c) Find the method-of-moments estimator of 0. (2) (d) Find the maximum likelihood estimator of 0. (7) QUESTION 4 [21]

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