inferential statistics-->

3. An assembly line returns a nished item every 10 seconds. Let Z, be equal to 1 if the i-th item is faulty, or 0 otherwise. The random variables Z1, Z2, . .. are assumed independent and identically distributed, with unknown fault probability p > 0. We are interested in characterising the mean 5' = lfp of the geometric population X1, X2, . . . , which denote the number of items up to and including the next faulty item. The corresponding probability mass function is: 1 1 31 fX($I9)=g(lE) :r=1,2,3,.. Note that, since a: 2 1, also a? I: 1. An observed sample X1, . . . ,Xo gives the average value E = 13.7. (a) Derive a 95% approximate condence interval for 19 centred around its max- imum likelihood estimator. You should show all your workings and give the nal numerical solution