45. A random variable X has the Weibull distribution W

(b,

c) if its density is C(X) "-l b t e -(x/b l ', X> 0,

b, C > O. (i) Show that this defines a probability density. (ii) If Xl"'" Xn is a sample from W

(b, c), with the shape parameter C known, show that there exists a UMP test of H : b bo against b > bo and give its form.