STAT 225 - Homework 1
Due Friday May 22
Comments:
1. This HW assignment covers the material discussed in the 5/18 lecture, and the 5/19 lecture
(up to and including page 6 in the handout)
2. This homework is due Friday, May 22 in class, BEFORE class start
36-225 - Homework 4 SOLUTIONS
1. 4 points: 2 for E(Y), 2 for V(Y)
The random variable of interest is Y , the number of successful explorations in n = 10 explorations. Then Y has a binomial distribution with p = .1. Hence
E (Y ) = np = 10(.1) = 1 and
V (Y
STAT 225 - Homework 6
Due Friday June 12
Comments:
1. This homework is due Friday, June 12 in class, BEFORE class starts.
2. Please remember staple if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may
36-225 - Homework 1 SOLUTIONS
1. 12 points: 2 for each part
(i) The document reaches its destination on time (i.e., on-time delivery by at least one of
the three services).
A1 A2 A3
(ii) The document does not reach its destination on time. A1 A2 A3 or A1
STAT 225 - Homework 2
Due Wednesday May 27
1. This homework is due Wednesday, May 27 in class, BEFORE class starts.
2. Please remember staple if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may not re
STAT 225 - Homework 4
Due Tuesday June 2
Comments:
1. This homework is due Tuesday, June 2 in class, BEFORE class starts.
2. Please remember staple if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may
36-225 - Homework 2 SOLUTIONS
1. 15 Points: 3 for each part (2 for work, 1 for numerical accuracy)
If two events, A and B, are such that P(A) = .5, P(B) = .3, and P(A B) = .1, nd the
following:
(a) P (A|B ) =
.1
1
P (A B )
=
=
P (B )
.3
3
(b) P (B |A) =
P
36-225 Introduction to Probability Theory Fall 2015
My Very Short Review of Some Math Topics
This document is meant to highlight certain mathematical techniques that are often used in 36-225.
In particular, it is not a general review of 1-D and 2-D calcul
Chapter 3
R: Using Scripts
In the rst two chapters, I showed how to interact with the R command line. But sometimes
you will want to accomplish tasks that are not optimally tackled by typing in command after
command. In this case, you use a script.
A scri
Chapter 1
Introduction to R
1.1
What Is R?
R is a software environment for statistical computing and graphics. Its interface is an interpreter, i.e., you type commands into the R window rather than writing full routines and then
compiling them (as in C).
Chapter 2
R: Data Entry and Plotting
2.1
Data Entry
Here, we assume we will always be entering data from a le in ASCII (human-eye-readable)
format. That will be true of all data les I provide on Blackboard this semester.
First, go to the Blackboard web si
36-225 Introduction to Probability Theory Fall 2015
Homework 9
Due Friday, November 13th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of Wackerly 7:
check the problem scans on Blackboard to en
36-225 Introduction to Probability Theory Fall 2015
Homework 1
Due Friday, September 11th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of Wackerly 7:
check the problem scans on Blackboard to e
36-225 Introduction to Probability Theory Fall 2015
Homework 6
Due Friday, October 16th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of Wackerly 7:
check the problem scans on Blackboard to ens
36-225 Introduction to Probability Theory Fall 2015
Homework 3
Due Friday, September 25th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of Wackerly 7:
check the problem scans on Blackboard to e
36-225 Introduction to Probability Theory Fall 2015
Homework 5
Due Friday, October 9th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of Wackerly 7:
check the problem scans on Blackboard to ensu
STAT 225 - Homework 3
Due Friday May 29
Comments:
1. This homework is due Friday, May 29 in class, BEFORE class starts.
2. Please remember staple if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may no
36-225 - Homework 3 SOLUTIONS
1
1. 19 points: 4 for E (Y ), 5 for E ( Y ), 5 for E (Y 2 1), 5 for V (Y )
E (Y ) =
yPY (y ) = 1(.4) + 2(.3) + 3(.2) + 4(.1) = 2.0
y
E
1
Y
=
y
1
1
1
1
PY (y ) = 1(.4) + (.3) + (.2) + (.1) = .6417
y
2
3
4
2
E (Y 1) = E (Y 2 )
STAT 225 - Homework 5
Due Thursday June 4
Do the following problems.
1. Let Y P oisson().
t 1)
(a) Show that the moment generating function of X is: MY (t) = e(e
Guidance:
ak
Youll have to use the following math fact:
= ea
k!
k=0
.
(b) Dierentiate the mgf
36-225 - Homework 5 SOLUTIONS
1. 16 points: (a) 8 points (b) 8 points (3 for E (Y ), 3 for E (Y 2 ) and 2 for V (X )
ety PY (y ) =
(a) MY (t) = E (etY ) =
y
(b) E (Y ) =
d
dt MY (t)|t=0
E (Y 2 ) =
y =0
= e(e
d2
MY (t)|t=0
dt2
ety
t 1)
y =0
(et )y
t
t
= e
36-225 - Homework 6 SOLUTIONS + Grading Key
1. 5 points: 3 for nding E (X 2 ), 2 for V(X)
Let X U (a, b). We already know that E (X ) =
b
x2
E (X 2 ) =
a
=
=
=
=
= V (X ) = E (X 2 ) E 2 (X ) =
a+b
. Then
2
1
dx
ba
1
x3
ba 3
b
a
1 b3 a3
ba 3
1 (b a)(b2 + a
STAT 225 - Homework 7
Due Tuesday June 16
Comments:
1. This homework is due Tuesday, June 16 in class, BEFORE class starts.
2. Please remember staple if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you ma