CHEMISTRY 102B
Practice Hour Exam I
Spring 2015
Dr. D. DeCoste
Name _
Signature _
T.A. _
This exam contains 17 questions on 5 numbered pages. Check now to make sure you
have a complete exam. You have
1. I choose a real number uniformly at random in the interval [2, 6], and call it X .
(a) Find the CDF of X, FX (x).
(b) Find EX .
2. Let X be a continuous random variable with the following PDF
f X (
1
Problems
1. Let X be a discrete random variable with the following PMF
1
for x = 0
2
1
for x = 1
3
1
PX (x) =
for x = 2
6
0
otherwise
(a) Find RX , the range of the random variable X .
(b) Find P (X
CHEMISTRY 102B
Practice Hour Exam II
Spring 2015
Dr. D. DeCoste
Name _
Signature _
T.A. _
This exam contains 22 questions on 8 numbered pages. Check now to make sure you have a
complete exam. You have
1
Problems
1. Suppose that the universal set S is dened as S = cfw_1, 2, , 10 and A = cfw_1, 2, 3,
B = cfw_X S : 2 X 7, and C = cfw_7, 8, 9, 10.
(a) Find A B
(b) Find (A C ) B
(c) Find A (B C )
(d) Do
CHAPTER 1. BASIC CONCEPTS
68
1.5
End of Chapter Problems
1. Suppose that the universal set S is dened as S = cfw_1, 2, , 10 and A = cfw_1, 2, 3,
B = cfw_X S : 2 X 7, and C = cfw_7, 8, 9, 10.
(a) Find
Chapter 3
Discrete Random Variables
3.1
3.1.1
Basic Concepts
Random Variables
In general, to analyze random experiments, we usually focus on some numerical aspects of the
experiment. For example, in a
1. Let X be a random variable with the following CDF:
0
x
FX (x) =
for x < 0
for 0 x <
x+
1
1
2
for
1
4
x<
for x
1
4
1
2
1
2
(a) Plot FX (x) and explain why X is a mixed random variable.
1
(b) Find
1
Problems
1. A coee shop has 4 dierent types of coee. You can order your coee in a small,
medium, or large cup. You can also choose whether you want to add cream, sugar,
or milk. In how many ways can
1. I choose a real number uniformly at random in the interval [2, 6], and call it X .
(a) Find the CDF of X, FX (x).
(b) Find EX .
Solution:
(a)
We saw that all individual points have probability 0; i
1
Problems
1. Let X be a discrete random variable with the following PMF
1
for x = 0
2
1
for x = 1
3
1
PX (x) =
for x = 2
6
0
otherwise
(a) Find RX , the range of the random variable X .
(b) Find P (X
1. Let X be a random variable with the following CDF:
0
x
FX (x) =
for x < 0
for 0 x <
x+
1
1
2
for
1
4
x<
for x
1
4
1
2
1
2
(a) Plot FX (x) and explain why X is a mixed random variable.
1
(b) Find
1
Problems
1. Let X be a discrete random variable with the following PMF
1
for x = 0
2
1
for x = 1
3
1
PX (x) =
for x = 2
6
0
otherwise
(a) Find RX , the range of the random variable X .
(b) Find P (X
1. Let X be a discrete random variable with the following PMF:
1
for x = 0
2
1
for x = 1
3
1
PX (x) =
for x = 2
6
0
otherwise
(a) Find RX , the range of the random variable X .
(b) Find P (X 1.5).
(c)
1. Consider two random variables X and Y with joint PMF given in Table 1.
Table 1: Joint PMF of X and Y in Problem 1
Y =1 Y =2
X=1
1
3
1
12
X=2
1
6
0
X=4
1
12
1
3
(a) Find P (X 2, Y > 1).
(b) Find the
1. I choose a real number uniformly at random in the interval [2, 6], and call it X .
(a) Find the CDF of X, FX (x).
(b) Find EX .
Solution:
(a)
We saw that all individual points have probability 0; i
1
Problems
1. I choose a real number uniformly at random in the interval [2, 6], and call it X .
(a) Find the CDF of X, FX (x).
(b) Find EX .
2. Let X be a continuous random variable with the followin
Solutions Manual for
Probability and Random Processes for
Electrical and Computer Engineers
John A. Gubner
University of WisconsinMadison
File Generated July 13, 2007
CHAPTER 1
Problem Solutions
1. =
CHEMISTRY 102B
Practice Hour Exam III
Spring 2015
Dr. D. DeCoste
Name _
Signature _
T.A. _
This exam contains 22 questions on 8 numbered pages. Check now to make sure you have a
complete exam. You hav
CHEMISTRY 102B
Practice Hour Exam II
Spring 2015
Dr. D. DeCoste
Name _
Signature _
T.A. _
This exam contains 22 questions on 8 numbered pages. Check now to make sure you have a
complete exam. You have
CHEMISTRY 102B
Hour Exam I
February 17, 2015
Dr. D. DeCoste
Name _
Signature _
T.A. _
This exam contains 17 questions on 6 numbered pages. Check now to make sure you
have a complete exam. You have one
Lecture 13
Heat Engines
Thermodynamic processes and entropy
Thermodynamic cycles
Extracting work from heat
- How do we define engine efficiency?
- Carnot cycle: the best possible efficiency
Reading
Lecture 16
Equilibrium and Chemical Potential
Free Energy and Chemical Potential
Simple defects in solids
Intrinsic semiconductors
Reference for this Lecture:
Elements Ch 11
Reference for Lecture 1
Miscellaneous Notes
The end is near dont get behind.
All Excuses must be taken to 233 Loomis
before 4:15, Monday, April 30.
The PHYS 213 final exam times are
* 8-10 AM, Monday, May 7
* 8-10 AM, Tue
Lecture 22
Freezing/boiling Point Elevation/depression
Supercooling/superheating
Midterm review
Phase Diagram:
p
Solid
Liquid
p3
p2
Gas
p1
T
Lecture 21, p 1
Phase Transitions and Volume Change
So far,
Miscellaneous Notes
The end is near dont get behind.
All Excuses must be taken to 233 Loomis
before 4:15, Monday, April 30.
The PHYS 213 final exam times are
* 8-10 AM, Monday, May 7
* 8-10 AM, Tue
Lecture 14
Heat Pumps, Refrigerators, and
Bricks!
Pumping Heat: Heat pumps and Refrigerators
Available Work and Free Energy
Work from Hot and Cold Bricks
Reading for this Lecture:
Elements Ch 10
Re
Miscellaneous Notes
The end is near dont get behind.
All Excuses must be taken to 233 Loomis
before 4:15, Monday, April 30.
The PHYS 213 final exam times are
* 8-10 AM, Monday, May 7
* 8-10 AM, Tue
Miscellaneous Notes
The end is near dont get behind.
All Excuses must be taken to 233 Loomis
before 4:15, Monday, April 30.
The PHYS 213 final exam times are
* 8-10 AM, Monday, May 7
* 8-10 AM, Tue