Statistical Theory (STAT 467/667)
Homework 1 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 3.2.13.
Let X1 , ., X7 be i.i.d. U(0, 1), that is independent and identically distributed with uniform distrib
Statistical Theory (STAT 467/667)
Homework 3 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 5.2.1.
8
ki (1 )1ki =
L()
=
ln L()
=
=
ki
(1 )8
8
i=1
ki
= 5 (1 )3
5 ln() + 3 ln(1 )
d
ln L()
d
8
i=1
5
3
+
(
Statistical Theory (STAT 467/667)
Homework 4 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 5.3.2
203
Let 52, 69, 73, 88, 87, 56 be the data describing female CH3 half-life. Then in order to construct a
Statistical Theory (STAT 467/667)
Homework 5 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 5.4.2.
u n1
1
From Example 5.4.2, f (u) = n
1
(a) For n = 6 and = 3, f (u) = 6 3
for 0 u .
u 5
3
=
3.2
2
5
24
Statistical Theory (STAT 467/667)
Homework 6 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 5.8.1.
Let X geometric(p) where pX (k | ) = (1 )k for k = 1, 2, . . . We are looking for the posterior distrib
Statistical Theory (STAT 467/667)
Homework 7 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 6.2.1.
(a) Compute z =
y
114.2 120
=
= 1.61. Reject H0 if z z0.08 = 1.41. Since 1.61 < 1.41, we
/ n
18/ 25
re
Statistical Theory (STAT 467/667)
Homework 8 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 6.4.8
Will n = 45 be a suciently large sample size to test H0 : = 10 versus H1 : = 10 at the = 0.05 level of
s
Statistical Theory (STAT 467/667)
Homework 9 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 7.3.4
(n 1)S 2
(n 1)2 Var(S 2 )
. Then Var(Y ) =
. We also know that Var(Y ) = Var(2 ) = 2(n 1). It follows
n1
Statistical Theory (STAT 467/667)
Homework 10 Solution - Spring 2015
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 9.2.7.
Let = 0.1. Then sp = 634.9 and t = 4.55. Since t = 4.55 < t0.05,148 z0.05 = 1.64, reject H0 .
Problem