Find the RaoCramr lower bound, and thus the asymptotic variance of the maximum likelihood estimator 6, if the random sample X1, X2, ... , Xn is taken from each of the distributions having the following pdfs: (a) f(x; ) = (1/ 2) x ex/ , 0 < x < , 0 << . (b) f(x; ) = (1/2 3) x2 ex/ , 0 < x < , 0 << . (c) f(x; ) = (1/) x(1)/ , 0 < x < 1, 0 << .

Tuesday, April 4 • Example 12: Sleeping Medication A research concludes that the number of hours of additional sleep by patients using Ambien increased on average by a statistically significant amount , 1.5 hours. What type of error might this be H :0 Ambien has no effect ; aH : Ambien increases sleep on average; rejected null a. This is a correct decision. The researchers concluded a significant increase in the number of hours of sleep, on av