STAT215: Homework 5
Due: Wednesday, April 18
1. (40 pt) The Neyman-Pearson lemma tells us that the optimal test of iid a point-null hypothesis H0 : cfw_Xi f0 (x) against a point-alternative iid H1 : cfw_Xi f1 (x) will reject H0 for large values of the l
Solutions for Homework 4
Due: Wednesday, March 28
1. (10 pt) Let X be a random variable having probability density f (x|) = expcfw_()Y (x) ()h(x), where is an increasing and dierentiable function of R. (a) Show that log l() log l(0 ) is increasing(or decr
STAT215: Homework 3
Due: Wednesday, Mar 06
1. (10 pt) Let (X1 , , Xn ) be a random sample of binary random variables with P (X1 = 1) = p, where p (0, 1) is unknown. Let be the MLE of = p(1 p). (i) Show that is asymptotically normal when p =
1 2 1 (ii) Whe
STAT215: Solutions for Homework 2
Due: Wednesday, Feb 14
1. (10 pt) Suppose we take one observation, X, from the discrete distribution, x 2 1 0 1 2 Pr(X = x|) (1 )/4 /12 1/2 (3 )/12 /4, 0 1 Find an unbiased estimator of . Obtain the maximum likelihood est
STAT215: Solutions for Homework 1
Due: Wednesday, Jan 30
1. (10 pt) For X Be(, ), (b) What is the MGF Mlog X (t) for the random variable Y := [log X]? [HINT: Integration by parts is not needed for (a), and no new calculations at all are needed for (b)!] S