qs1 1. Let X1,,Xn be a random sample from a distribution with density f(x;)=2xex2/1(0,)(x),>0 Answer the following using the fact that Yi=Xi2mxp(). (a) Show that that 2i=1nXi2/ is a pivotal quantity for . (c) Use (b) to obtain a 100(1)% interval estimator of =()=1/. Hint: () is a monotonically decreasing function of ..

1. qs1
1. Let X1,,Xn be a random sample from a distribution with density f(x;)=2xex2/1(0,)(x),>0 Answer
the following using the fact that Yi=Xi2mxp(). (a) Show that that 2i=1nXi2/ is a pivotal quantity for .
(c) Use (b) to obtain a 100(1)% interval estimator of =()=1/. Hint: () is a monotonically decreasing
function of .