STAT 4101 (Fall 2014) Homework 2
Due: Wednesday, September 17
Directions: Show all work for each problem below. Do not use software! Provide exact solutions
(not decimal approximations) to each of the problems requiring a numeric answer.
1. Textbook Probl
STAT 4101 (Spring 2016) Homework 3
Due: Wednesday, February 17
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a nu
STAT 4101 (Spring 2016) Homework 4
Due: Wednesday, March 9
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numeri
STAT 4101 (Fall 2016) Homework 5
Assigned: Wednesday, October 12
Due: Wednesday, October 19
1. Textbook Problems: 3.62, 3.66(a), 3.67, 3.68, 3.84, 3.88, 3.127, 3.133, 3.141,
2. Two teams, Team A and Team B, will play 7 independent games against each other
STAT : Theory of Statistics I
Yuwen Gu
September ,
Theory of Statistics, Fall , Yuwen Gu
/
Words of Advice
Read textbook sections, preferably before class
Review class notes
Do the textbook problems
Do the written-out problems
You should begin early so t
STAT 4101 (Fall 2016) Homework 6
Assigned: Wednesday, October 19
Due: Wednesday, October 26
Directions: Show all work for each problem below. Do not use software! Provide exact solutions
to each of the problems requiring a numeric answer. You may also inc
STAT 4101 (Fall 2012) Homework 3
Due: Wednesday, September 26
1. Textbook Problems: 2.86, 2.96, 2.112, 2.120, 2.124, 2.134
2. A sample space consists of 4 sample points with associated probabilities given by p, 2p, 3p
and 13 . Find the value of p.
n
3. Fi
Homework Three Solutions
Exercise 2.86 (p. 59)
Solution.
(a) No. It follows from P (A B) = P (A) + P (B) P (A B) 1.
(b) P (A B) 0.5.
(c) No.
(d) P (A B) 0.70.
Exercise 2.96 (p. 60)
Solution. Using the results of Ex. 2.95:
(a) 0.5 + 0.2 (0.5)(0.2) = 0.6.
(
STAT 4101 (Fall 2012) Homework 9
Due: Wednesday, November 14
1. Textbook Problems: 5.52, 5.58, 5.60, 5.74, 5.76, 5.82, 5.92, 5.94, 5.99
2. Suppose p is a fixed number in the interval [0, 1]. Let Y be a random variable with the
following density:
f (y) = p
STAT 4101 (Fall 2012) Homework 8
Due: Wednesday, November 7
1. Textbook Problems: 4.137, 4.140, 4.141, 5.6, 5.8, 5.14, 5.18, 5.26, 5.32
2. Let X Exp(). Confirm that E(X) = and VAR(X) = 2 using its MGF:
mX (t) =
1
1 t
t<
1
3. Suppose that X has the followi
STAT 4101 (Fall 2012) Homework 4
Due: Wednesday, October 3
1. Textbook Problems: 3.6, 3.24, 3.30, 3.33, 3.44, 3.56, 3.66(a), 3.70, 3.82, 3.108, 3.118
2. A random variable X takes 3 possible values, and its distribution is defined as:
1
1
1
P (X = 2) = , P
STAT 4101 (Fall 2012) Homework 1
Due: Wednesday, September 12
Directions: Show all work for each problem below. Do not use software! Provide exact solutions
(not decimal approximations) to each of the problems requiring a numeric answer.
1. Textbook Probl
!
!
!
!
!
!
!
!
!
!
Problem 1
Solution.
(a) First, note that if X Exp( ), then the MGF of X is
Z 1
1
1
1
mX (t) = E(etX ) =
etx e x/ =
,t< ,
1
t
0
and if Y Gamma(, ), then the MGF of Y is
Z 1
1
mY (t) = E(etY ) =
ety
y
()
0
1
x/
e
=
1
(1
t)
,t<
1
.
iid
S
STAT 4101 (Spring 2016) Homework 8
Due: Wednesday, May 4
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numeric
STAT 4101 (Spring 2016) Homework 7
Due: Wednesday, April 27
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numer
STAT 4101 (Spring 2016) Homework 8
Due: Wednesday, May 4
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numeric
STAT 4101 (Spring 2016) Homework 5
Due: Wednesday, March 30
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numer
STAT 4101 (Spring 2016) Homework 2
Due: Wednesday, February 10
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a nu
STAT 4101 (Spring 2016) Homework 4
Due: Wednesday, March 9
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numeri
STAT 4101 (Spring 2016) Homework 6
Due: Wednesday, April 13
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numer
STAT 4101 (Spring 2016) Homework 1
Due: Wednesday, February 3
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a num
STAT 4101 (Spring 2016) Homework 7
Due: Wednesday, April 27
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numer
STAT 4101 (Spring 2016) Homework 6
Due: Friday, April 15
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numeric
STAT 4101 (Spring 2016) Homework 1
Due: Wednesday, February 3
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a num
STAT 4101 (Spring 2016) Homework 5
Due: Wednesday, March 30
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a numer
STAT 4101 (Spring 2016) Homework 2
Due: Wednesday, February 10
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a nu
STAT 4101 (Spring 2016) Homework 3
Due: Wednesday, February 17
Directions: Show all work for each problem below and explain your answer fully. Do not use
software! Provide exact solutions (not decimal approximations) to each of the problems requiring
a nu
!
!
!
!
Problem 2
Solution. In the simplePlinear regression setting, 0 and 1 are the minimizer of the residual sum of
n
2
squares RSS( 0 , 1 ) = i=1 (yi
0
1 xi ) . Thus,
@RSS( 0 , 1 )
=
@ 0
@RSS( 0 , 1 )
=
@ 1
Therefore, it can be solved that
1 =
where x
STAT 4101 (Fall 2012) Homework 6
Due: Wednesday, October 24
Directions: Provide exact solutions to all problems that require a numeric answer. Do not provide
decimal approximations! Show all work to receive full credit.
Textbook Problems: 4.18, 4.24, 4.26
Homework Seven Solutions
Exercise 4.70 (p. 183)
Solution. From Ex. 4.68, the proportion of students with a GPA greater than 3.0 is 0.2266. Set X = #
of students in the sample with GPA greater than 3.0. Thus, X is binomial with n = 3 and p = 0.2266.
Then,