Question: QUESTION 4 Let X1, X2,..., X be a random sample of size n from with the probability density function 4x 4 f (x ) e

QUESTION 4 Let X1, X2,..., X be a random sample of size n from with the probability density function 4x 4 f (x ) e , x>0 O , elsewhere Show that the moment generating function for X is Mx (t) = 1-- 22 a) 4 (6 marks) 8EX b ) Find the sampling distribution of W = 1=1 and hence state the distribution of W. 22 (5 marks) C) Construct a 100(1-a )% confidence interval for 12 (4 marks) 20 d) If EX, = 100, find a 95% confidence interval for 12. 1=1

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