Homework 4
MAP 6111
Mathematical Statistics. Solutions to Homework 4
Problem 8.12 For samples of size n = 1, 4, 16, 64, 100 from an normal population with mean and known variance
2 , plot the power function of the following LRTs. Take = 0.05.
(a) H0 : 0
Mathematical Statistics. Homework 2
Chapter 4, # 10. the random pair (X, Y ) has the distribution
X
2
1
Y
1
12
1
6
2
3
4
0
1
6
0
1
3
3
1
12
1
6
0
1. Show that X and Y are dependent.
The marginal pmf distributions for X and Y are given by
1
fX (1) = 12 +
Homework 5
MAP 6111
Mathematical Statistics. Solutions to Homework 5
Problem 9.2 Let X1 , . . ., Xn be iid N ( , 1). A 95% condence interval for is x 1.96/ n. Let p denote the
probability that an additional independent observation, Xn+1 , will fall in thi