Let X,,X2,..., X, be a random sample of size n from with the probability density function 4x f(x)=: e ,x >0 ,elsew here a) Show that the moment generating function for X is Mx (t) (6 marks) 8 x, b) Find the sampling distribution of W i=1 and hence state the distribution of W. 22 %3D (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 22. %3D i-1 (5 marks)