MATH 32
Worksheet 03: Chapters 34
Spring 2012
1. A survey of people in a given region showed that 20% were smokers. The probability of death
due to lung cancer, given that a person smoked, was roughly 10 times the probability of death
due to lung cancer,
Midterm 2, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 10 problems that will count for a total
of 100 points. You are allowed to use a cheat sheet, which is defined to be one 8.5 inch by 11 inch, doublesided, hand
MATH 32 Midterm 1
Fall Semester 2008
Duration: 50 minutes
Instructions: Answer all questions, without the use of notes, books or calculators. Partial credit
will be awarded for correct work, unless otherwise specied. The total number of points is 100.
1.
MATH 32
Worksheet 00: Review of Math: 21,22,23
Fall 2016
1. Find the value of p that maximizes
S(p) = p ln p (1 p) ln(1 p).
2. Evaluate the integral or show that it is divergent.
Z
Z
x
(a)
xe dx
(b)
0
Z
Z
x dx
x2 + 1
(c)
(d)
1
dx
+1
x2
dx
x
3. Evaluate t
MATH 32
Worksheet 04: Chapter 4
Fall 2016
1. A satellite system consists of 4 components and can function adequately if at least 2 of the
4 components are in working condition. If each component is, independently, in working
condition with probability 0.6
MATH 32
Worksheet 02: Chapters 3
Fall 2016
1. R Exercise: Coin toss simulation. We discussed how computer can be used to simulate
chance events. We can use these simulation to validate some of the probability calculations.
The Law of Large Numbers says th
MATH 32
Worksheet 01: Chapter 2
Fall 2016
To solve the problems 16, I suggest the following strategy:
(i) describe the sample space by listing all possible outcomes or by describing precisely what each
element looks like;
(ii) describe which subset repres
MATH 32
Worksheet 03: Chapters 4
Fall 2016
1. R Simulation: For the following simulation write down the results that you obtained and
the meaning of the results. How do these results compare to the theoretical prediction?
(Problem 5 Homework 1: )A ball is
# Solutions for HW 11
# Question 1
# load data set
load('timber.RData')
# iqr for density
iqr.density = quantile(x=timber$Density,probs=0.75,type=6) quantile(x=timber$Density,probs=0.25,type=6)
# iqr for hardness
iqr.hardness = quantile(x=timber$Hardness,
Name:_
SID:_
Section:_
Midterm Exam #1-Math 032-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No notes are permitted, but calculators are.
Show your work.
Problem #1 (10 points)
A data set consists of 2 unknown values x and y as well as 0, fo
MATH 32 Midterm 2
Fall Semester 2008
Duration: 50 minutes
Instructions: A cheat sheet on one side of a 8.5x11 page is allowed and must be turned in with
the exam. A calculator is allowed as well. Partial credit will be awarded for correct work, unless
oth
MATH 32 Midterm 2
Spring Semester 2009
Duration: 50 minutes
Instructions: Answer all questions, without the use of notes or books. Calculators may be used to
calculate numbers only. Partial credit will be awarded for correct work, unless otherwise specied
MATH 32 Midterm 1
Spring Semester 2009
Duration: 50 minutes
Instructions: Answer all questions, without the use of notes, books or calculators. Partial credit
will be awarded for correct work, unless otherwise specied. The total number of points is 80.
1.
MATH 32 Final Exam
Spring Semester 2009
Duration: 3 hours
Instructions: Answer all questions, without the use of notes or books. Calculators may be used to
calculate numbers only. Partial credit will be awarded for correct work, unless otherwise specied.
Name:_
SID:_
Section:_
Final Exam -Math 032-F 07
The exam is 50 minutes long. No notes are permitted, but calculators are.
Show your work.
Problem
1
2
3
4
5
6
7
8
Total
Score out
of 10
1. Find three numbers whose sample mean is 2 and whose sample variance
Name:_
SID:_
Section:_
Midterm Exam #2-Math 032-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No notes are permitted, but calculators are.
Show your work.
Problem #1
Let A=cfw_It rains and let B=cfw_It pours. Transcribe the following
statemen
Name:_
SID:_
Section:_
Midterm Exam #3-Math 032-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No notes are permitted, but calculators are.
Show your work.
Problem
1
2
3
4
5
Total
Score out
of 10
Problem #1
Fifty tickets labeled 1 through 50 a
MATH 32 Final Exam
Fall Semester 2008
Duration: 3 hours
Instructions: A cheat sheet on one side of a 8.5x11 page is allowed and must be turned in with
the exam. A calculator is allowed when adding, subtracting, multiplying, dividing, and calculating the m
HW 7 Solutions, Math 32, Spring 2016, Prof. Bhat
1. We see that U must be in the interval (0, 1)remember that because U
is a continuous random variable, there is no probability that U exactly
equals either 0 or 1. If you have any doubt about this, integra
HW 1 SOLUTIONS, Math 32, Spring 2016, Prof. Bhat
1. Calculate
Z
1
|x| dx.
1
Solution: Keep in mind that
(
x
x0
|x| =
x x 0.
With that in mind, we see that:
Z 1
Z 0
Z 1
|x| dx =
|x| dx +
|x| dx
1
1
0
Z 0
Z 1
=
(x) dx +
x dx
1
0
0
1
x2
x2
= +
2 1
2 0
1 1
Probability-Statistics Glossary
Math 32, Spring 2016, Prof. Bhat
Probability
Statistics
X is a random variable. We start with certain
knowledge regarding the PDF f (x) and/or
the CDF F (x) of X. Using this knowledge and the
methods in Chapter 6, we can ge
Midterm 1 Version 2, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 16 problems that will count for a total
of 100 points. No calculators, books, or electronic devices of any kind are allowed. When you turn in your
S
Midterm 2, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 10 problems that will count for a total
of 100 points. You are allowed to use a cheat sheet, which is defined to be one 8.5 inch by 11 inch, doublesided, hand
Midterm 2, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 10 problems that will count for a total
of 100 points. You are allowed to use a cheat sheet, which is defined to be one 8.5 inch by 11 inch, doublesided, hand
Midterm 1, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 16 problems that will count for a total
of 100 points. No calculators, books, or electronic devices of any kind are allowed. When you turn in
your Scantron, y
Midterm 2, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 10 problems that will count for a total
of 100 points. You are allowed to use a cheat sheet, which is defined to be one 8.5 inch by 11 inch, doublesided, hand
Midterm 1 Version 3, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 16 problems that will count for a total of 100
points. No calculators, books, or electronic devices of any kind are allowed. When you turn in your S
Everything You Always Wanted to Know About Empirical Quantiles but
Were Afraid to Ask: The Books Version, Rs Version, and All That Jazz
Math 32, Spring 2016, Prof. Bhat
The goal of these notes is to give you a better understanding of empirical quantiles.
Math 32, Monday, 4/18/16, Prof. Bhat
Linear regression: the simple y versus x case with no vectors and no matrices.
Lets say you are given n data points cfw_(xi , yi )ni=1 . The points lie in the plane. Youd like to
find the least squares line of best fit
Midterm 1 Version 4, Math 32, Fall 2016
Instructions: you have 50 minutes to complete this exam. There are 16 problems that will count for a total
of 100 points. No calculators, books, or electronic devices of any kind are allowed. When you turn in your
S
# HW 10 Solutions
# Problem 1
bincount = 935
binwidth = 41.5-40.5
# total number of data points
numdata = 5732
# we derived the following formula in lecture,
# to ensure the total area represented by the histogram equals 1
binheight = bincount/(binwidth*n
HW 6 SOLUTIONS, Math 32, Spring 2016
1. True/False: For any random variable X, the expected value E[X] is
always finite
Solution: False. Consider a continuous, coin-flip experiment in which
one gets paid 2n dollars, where n is the number of heads one got.
HW 9 SOLUTIONS, Math 32, Spring 2016
1. Recall the relation between degrees Celsius and degrees Fahrenheit degrees
Fahrenheit =
9
degrees Celsius + 32.
5
Let X and Y be the average daily temperatures in degrees Celsius in Amsterdam and
Antwerp. Suppose th
HW 3 Solutions, Math 32, Spring 2016, Prof. Bhat
1. A ball is drawn at random from an urn containing one red and one
white ball. If the white ball is drawn, it is put back into the urn. If
the red ball is drawn, it is returned to the urn together with two
HW 5 Solutions, Math 32, Spring 2016, Prof. Bhat
1. The probability that the student fails the exam is
P (X < 0.55)
where X is a random variable whose PDF is the function f (x) given in
the problem. To calculate P (X < 0.55), we must integrate as follows: