Probability and Statistics II

Instructor: Dr. Jesse Crawford Office phone: (254) 968-9536

Email: Office: Math 332

Website: faculty.tarleton.edu/crawford

Office Hours:

MWF 10:00 – 11:00 and 1:00 – 2:00, or by appointment. You are highly encouraged to visit my office for help.

Course Meeting Times: MWF 9:00 – 9:50 in Math 212

Required Materials: We will cover chapters 4–7 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 TI-nspire CAS.

Exams: There will be three exams during the semester and a cumulative final exam.

Homework: Homework will be assigned almost every day, and it will usually be due 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.

Percentage
of Grade / Average / Grade
Homework / 20% / 90-100 / A
Exam 1 / 20% / 80-89 / B
Exam 2 / 20% / 70-79 / C
Exam 3 / 20% / 60-69 / D
Final Exam / 20% / 0-59 / 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 submit up to two late homework assignments during the semester, 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 . Student Disability Services is located in Math 201. More information can be found at 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.

How to Succeed in This Course:

1)Attend Class. Only miss class when absolutely necessary.

2)Pay attention during class.

3)Start homework as soon as possible. Don’t procrastinate.

4)Get help on problems that you are struggling with, either from me, the math clinic, or other students.

5)Study a moderate amount before exams.

Student Learning Outcomes:

Knowledge Outcomes: Students will demonstrate knowledge of the following topics by performing calculations, solving applied problems, and writing basic proofs.

  1. The central limit theorem, sampling distributions, and normal approximations to discrete distributions.
  2. The bivariate normal distribution and univariate linear regression.
  3. Unbiasedness and sufficiency.
  4. Bayesian estimation.
  5. Likelihood ratio tests and uniformly most powerful tests.

Skill Outcomes: Students will demonstrate proficiency in the following skills:

  1. Calculating probabilities and percentiles for the normal distribution and Student’s distribution.
  2. Producing descriptive statistics, such as the sample mean and variance, histograms, and box-plots.
  3. Maximum likelihood estimation.
  4. Obtaining confidence intervals for population means and proportions, including the calculation of adequate sample sizes.
  5. Performing hypothesis tests for population means and proportions.
  6. Performing hypothesis tests for contingency tables, univariate linear regression, and analysis of variance.

Sections of Primary Interest

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

5. Distributions of Functions of Random Variables

5.1 Functions of One Random Variable

5.2 Transformations of Two Random Variables

5.3 Several Independent Random Variables

5.4 The Moment-Generating Function Technique

5.5 Random Functions Associated with Normal Distributions

5.6 The Central Limit Theorem

5.7 Approximations for Discrete Distributions

6. Estimation

6.1 Point Estimation

6.2 Confidence Intervals for Means

6.3 Confidence Intervals for Difference of Two Means

6.4 Confidence Intervals for Variances

6.5 Confidence Intervals for Proportions

6.6 Sample Size.

6.7 A Simple Regression Problem

6.8 More Regression

7. Tests of Statistical Hypotheses

7.1 Tests about Proportions

7.2 Tests about One Mean

7.3 Tests of the Equality of Two Means

7.4 Tests for Variances

7.5 One-Factor Analysis of Variance

7.6 Two-Factor Analysis of Variance

7.7 Tests Concerning Regression and Correlation