Probability and Statistics I
Instructor: Dr. Jesse Crawford
Email: jcrawford@tarleton.edu
Website: faculty.tarleton.edu/crawford
Office phone: (254) 968-9536
Office: Math 332
Office Hours:
MW 3:30 – 4:30
TR
2:30 – 3:30
F
2:00 – 3:00
You are highly encouraged to visit my office for help.
Course Meeting Times: MW 2:00 – 3:15 in Math 212
Required Materials: We will cover chapters 1-4 in Probability and Statistical Inference, 8th
ed., by Hogg and Tanis. You will also need a graphing calculator, such as a TI-83 Plus or a TInspire CAS.
Exams: There will be three exams during the semester and a cumulative final exam.
Homework: Homework will be assigned almost every day and collected two class periods later.
It is crucial to keep up with the homework to succeed in this course.
Grades: The following tables show how your final grade will be calculated.
Homework
Exam 1
Exam 2
Exam 3
Final Exam
Percentage
of Grade
20%
20%
20%
20%
20%
Average
Grade
90-100
80-89
70-79
60-69
0-59
A
B
C
D
F
Missed Exams and Late Homework: A student who misses an exam for a valid reason, such
as serious illness or the death of a family member will be allowed to make up the exam.
Students who make up exams are required to provide documentation confirming that the absence
occurred for a legitimate reason. You may turn in up to two homework assignments late, and a
few homework assignments will be dropped.
Students with Disabilities: It is the policy of Tarleton State University to comply with the
Americans with Disabilities Act and other applicable laws. If you are a student with a disability
seeking accommodations for this course, please contact Trina Geye, Director of Student
Disability Services, at 254.968.9400 or geye@tarleton.edu. Student Disability Services is located
in Math 201. More information can be found at www.tarleton.edu/sds or in the University
Catalog.
Academic Integrity: The Tarleton University Mathematics Department takes academic
integrity very seriously. The usual penalty for a student caught cheating includes an F in the
course. Further penalties may be imposed, including expulsion from the university.
Student Learning Outcomes:
Knowledge Outcomes: Students will demonstrate knowledge of the following topics
by performing calculations, solving applied problems, and writing basic proofs.
a. Probability axioms and fundamental properties.
b. Conditional probability, statistical independence, and Bayes’s Theorem.
c. Characteristics and applications of the binomial, Poisson, uniform, exponential,
gamma, and chi-square distributions.
d. Marginal and conditional distributions for multivariate random variables.
e. Expected value, variance, and moment-generating functions of linear
combinations of independent random variables.
Skill Outcomes: Students will demonstrate proficiency in the following skills:
f. Counting techniques.
g. Calculation of probabilities for univariate random variables, using a probability
mass function, probability density function, or cumulative distribution function.
h. Calculation of expected value, variance, and other moments for univariate random
variables directly or by using the moment-generating function.
i. Transformations of univariate random variables.
j. Calculation of probabilities for multivariate random variables, using a joint
probability mass function or joint probability density function.
k. Calculation of expected values in the multivariate setting, including the
covariance and correlation coefficient of two random variables.
Sections of Primary Interest
1. Probability
1.1 Basic Concepts
1.2 Properties of Probability
1.3 Methods of Enumeration
1.4 Conditional Probability
1.5 Independent Events
1.6 Bayes's Theorem
2. Discrete Distributions
2.1 Random Variables of the Discrete Type
2.2 Mathematical Expectation
2.3 The Mean, Variance, and Standard Deviation
2.4 Bernoulli Trials and the Binomial Distribution
2.5 The Moment-Generating Function
2.6 The Poisson Distribution
3. Continuous Distributions
3.1 Continuous-Type Data
3.2 Exploratory Data Analysis
3.3 Random Variables of the Continuous Type
3.4 The Uniform and Exponential Distributions
3.5 The Gamma and Chi-Square Distributions
3.6 The Normal Distribution
3.7 Additional Models
4. Bivariate Distributions
4.1 Distributions of Two Random Variables
4.2 The Correlation Coefficient
4.3 Conditional Distributions
4.4 The Bivariate Normal Distribution