Welcome to the Stats 420 home page

Or, you can catch me in my office. My office is room 205C, Cockins Hall. My phone number is 292-5843. My office hours are on Monday, from 2:30 - 4:18. You can also catch me at other times.

The course TA is Fangfang Sun. Fangfang's office is MA 450. Her phone number is 292-9283. Her office hours are Tuesday from 10:30 - 11:30 and Wednesday from 2:30 - 3:30. Her email is fangfang@stat.osu.edu.

Reading Assignments

• Week One.

  The first week of the course is a short one. We'll get a start on the basics of probability through counting problems and with a few definitions.

• Lecture 1. Wednesday, September 23. Introduction.

  Introduction to the course, course policies. Definitions: experiment, sample space, outcome, event, intersection, union, complement, rules of probability. Reading assignment: 2.1 - 2.4.

• Recitation 1. Thursday, September 24. Counting Problems.

  Counting principles. Examples of counting problems. Reading assignment: Chapter 1.

• Lecture 2. Friday, September 25. Conditional Probability and Independence.

  Definition of conditional probability, uses of conditional probability, definition and use of independence. Reading assignment: 2.5 - 2.7.

• Week Two.

  During the second week of the course, we will learn a few more techniques for computing probabilities--notably the Law of Total Probability and Bayes' Theorem. We will also move from consideration of probabilities of events described in words to probabilities of events described by numbers, and hence to random variables.

• Lecture 3. Monday, September 28. Bayes' Theorem.

  Probability examples, easy and hard ways to do problems, extensible and non-extensible ways to do problems, the Law of Total Probability, Bayes' Theorem, examples. Reading assignment: 2.8.

• Lecture 4. Wednesday, September 30. Discrete Random Variables.

  Definition of a random variable, the probability distribution, the cumulative probability distribution (distribution function), properties of the probability distribution and the distribution function. Reading assignment: 3.1 - 3.2.

• Recitation 2. Thursday, October 1. Calculus Review.

  Questions related to homework problems. Review of a few calculus facts.

• Lecture 5. Friday, October 2. Continuous Random Variables.

  Continuous random variables, the probability density function (pdf), the cumulative distribution function (cdf), examples. Reading assignment: 3.3 - 3.4.

  Note! The lectures will depart a bit from the text over the next few days. We first trace through the development of multivariate distributions for discrete random variables. We will then return to cover the same concepts and objects for continuous random variables.

• Week Three.

  In the third week, we will continue our study of random variables. We will cover the basics of joint distributions--the distribution of two or more random variables--and the necessary concepts of marginal distributions and conditional distributions. Toward the end of the week, we will nibble on further properties of random variables.

• Lecture 6. Monday, October 5. Multivariate Distributions.

  The joint probability distribution, properties of joint probability distributions, joint probability density functions, the joint distribution function, extensions to more than two dimensions. Reading assignment: 3.5.

• Lecture 7. Wednesday, October 7. Marginal and Conditional Distributions.

  The marginal distribution, the marginal density, the conditional distribution, the conditional density, independence of random variables, dependence of random variables. Reading assignment: 3.6 - 3.7.

• Recitation 3. Thursday, October 8. Marginal and Conditional Distributions.

  Questions related to homework problems. Work with marginal and conditional distributions.

• Lecture 8. Friday, October 9. The Expected Value.

  The expected value of a random variable (a.k.a. the mean), the expected value of a function of a random variable, the expected value of a function of more than one random variable. Reading assignment: 4.1 - 4.2.

• Week Four.

  In the fourth week, we will work with the expected value and other moments of a random variable. One particularly interesting result is Chebyshev's Inequality. A useful device is the moment generating function. We'll cover these and more. We will also have the first midterm exam on Friday.

• Lecture 9. Monday, October 12. Moments of Random Variables.

  The variance, higher order central moments, higher order absolute moments, Chebyshev's inequality, the moment generating function. Reading assignment: 4.3 - 4.5.

• Lecture 10. Wednesday, October 14. Linear Combinations or Random Variables.

  The mean and variance of a linear combination of random variables, the conditional mean and variance. Reading assignment: 4.6 - 4.8.

• Recitation 4. Thursday, October 15. Exam Prep.

  Questions related to homework problems. Questions related to exam material.

• Lecture 11. Friday, October 16. Midterm Exam I.

  Coverage - Chapters 1 through 3. Exam rules as described in class.

• Week Five.

  During week five, we will review the midterm exam and begin to take a look at families of random variables. The first families that we will look at are based a a simple notion--an experiment as simple as a single flip of a coin. This simple experiment generates a host of probability distributions as we hook a collection of these mini-experiments (or trials) together.

• Lecture 12. Monday, October 19. Midterm Review.

  Review of midterm exam. Different strategies for various problems, including different approaches to counting problems. The discrete uniform distribution.

• Lecture 13. Wednesday, October 21. Discrete Random Variables - I.

  The Bernoulli trial. The binomial distribution. Relaxing the assumptions of the binomial distribution: not a fixed number of trials. The geometric distribution. Reading assignment: 5.1 - 5.4.

• Recitation 5. Thursday, October 22. Exam Prep.

  Questions related to homework problems. Discrete random variables.

• Lecture 14. Friday, October 23. Discrete Random Variables - II.

  The negative binomial distribution. Relaxing the assumptions of the binomial distribution: dependent trials. The hypergeometric distribution. Reading assignment: 5.5 - 5.6.

• Week Six.

  In the sixth week of the class, we will cover quite a number of probability distributions. Further discrete distributions include the Poisson and multinomial distributions. Continuous distributions include the related collection of the gamma distributions, the exponential distributions and the chi-square distributions. We will also see the beta distribution and the normal distribution.

• Lecture 15. Monday, October 26. Discrete Random Variables - III.

  Relaxing the assumptions of the binomial distribution: changing theta. The Poisson distribution. Relaxing the assumptions of the binomial distribution: more than two categories. The multinomial distribution. Reading assignment: 5.7 - 5.8.

• Lecture 16. Wednesday, October 28. Continuous Random Variables - I.

  The uniform distribution. The exponential distribution. Uses of the moment generating function. The gamma distribution. The chi-square distribution. Reading assignment: 6.1 - 6.3.

• Recitation 6. Thursday, October 29. Several Step Problems.

  Questions related to homework problems. Examples of "several step" problems.

• Lecture 17. Friday, October 30. Continuous Random Variables - II.

  The beta distribution. The normal distribution. Uses of the normal distribution. Probability calculations. Percentiles. Reading assignment: 6.4 - 6.6.

• Week Seven.

  In the seventh week, we will continue to work with distributions. First up is the bivariate normal distribution, a particularly important joint distribution. The bivariate normal distribution underlies much work in the area of regression--strongly connected to fitting lines by least squares. Next, we consider transformations, covering two of the three main techniques to move from one variable to another variable. The focus here is on finding the probability density function of the new variable.

• Lecture 18. Monday, November 2. The Bivariate Normal Distribution.

  The bivariate normal distribution. Marginal distributions. Conditional distributions. The distribution of a linear combination of the components. Reading assignment: 6.7.

• Lecture 19. Wednesday, November 4. Basic Transformations.

  Transformations for discrete random variables. The distribution function method of transformations. Examples of the transformation. Reading assignment: 7.1 - 7.2.

• Recitation 7. Thursday, November 5. Random Variables.

  Questions related to homework problems. Examples of calculations involving random variables.

• Lecture 20. Friday, November 6. Change of Variable Transformations.

  Linear transformations. The change of variables for increasing functions. Change of variables for decreasing functions. Two-to-one functions. Reading assignment: 7.3.

• Week Eight.

  In the eighth week, we will continue to study transformations. Transformations in several dimensions are particularly challenging, as there are quite a few potential pitfalls. We will round out the week with some streamlined calculations that can be performed with the help of moment generating functions.

• Lecture 21. Monday, November 9. Change of Variables in Several Dimensions.

  The change of variables. The Jacobian. The expression for the density of the transformed variates. Marginalization. Reading assignment: 7.4.

• Lecture 22. Wednesday, November 11. Veteran's Day.

  University Holiday. Enjoy the break.

• Recitation 7. Thursday, November 12. Transformations.

  Questions related to homework problems. Examples of transformations.

• Lecture 23. Friday, November 13. Moment Generating Functions.

  Moment generating functions and independent random variables. The sum of several variables. Poissons, gammas, and normals. The mean of several variables. Reading assignment: 7.5.

• Week Nine.

  In the ninth week, we will begin the transition from probability to statistics. The first step is to lay out the central limit theorem. The central limit theorem relies on the notion of a random sample. After we describe appropriate definitions and results, we can consider how to sample a finite population and how results must be adjusted to apply in this situation. From there, we will begin to look at the chi-square distribution.

• Lecture 24. Monday, November 16. The Law of Large Numbers.

  A random sample from an infinite population. The sampling distribution of the sample mean. Chebyshev's inequality and the law of large numbers. Reading assignment: 8.1 - 8.2.

• Lecture 25. Wednesday, November 18. The Central Limit Theorem.

  The central limit theorem. Proof of the CLT. Implications of the CLT. Reading assignment: 8.2.

• Recitation 8. Thursday, November 19. Transformations.

  Questions related to homework problems. Examples of transformations.

• Lecture 26. Friday, November 20. Finite Population Sampling.

  A simple random sample from a finite population. Definition of the population mean and variance. Estimation of the population mean and variance. Contrast to sampling from an infinite population. Examples, concerns, and cautions of finite population sampling. Reading assignment: 8.3.

• Week Ten.

  We kick the tenth week off with the second midterm exam. We will cover the chi-square distribution on Wednesday, and then it's a break for Thanksgiving.

• Lecture 27. Monday, November 23. Midterm Exam II.

  Coverage - Chapters 4 through 7. Exam rules as described in class.

• Lecture 28. Wednesday, November 25. The Chi-Square Distribution.

  The chi-square distribution. Its connection to the sample mean and sample variance of a random sample of normal variates. Uses of the chi-square distribution. Reading assignment: 8.4.

• Recitation 9. Thursday, November 26. Thanksgiving Holiday.

  The University is closed for the Thanksgiving holiday. Enjoy the break.

• Lecture 29. Friday, November 27. Thanksgiving Holiday.

  The University is closed for the Thanksgiving holiday. Enjoy the break.

• Week Eleven.

  The last week of the course. This week, we will learn about a pair of useful distributions--the t distribution and the F distribution--and we will wrap up the course.

• Lecture 29. Monday, November 30. The t distribution.

  The t distribution. Connection to the normal distribution and the chi-square distribution. How it arises from a random sample from the normal distribution. Uses of the t distribution. Reading assingment: 8.5.

• Lecture 30. Wednesday, December 2. The F distribution.

  The F distribution. Connection to the chi-square distribution. How it is connected to the normal distribution. Uses of the F distribution. Reading assignment: 8.6.

• Recitation 10. Thursday, December 3. Thanksgiving Holiday.

  Working with the new distributions--the chi-square, t, and F.

• Lecture 31. Friday, December 4. Course Wrap-Up.

  Course overview and wrap-up.

Course documents

• The course syllabus

• Homework 1. Due Friday, October 2.

  From the text, problems 1.31, 1.37, 1.55, 2.1 (a,b), 2.2 (b), 2.40, 2.43, 2.46, 2.62, 2.76, 2.77, 2.100.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw1soln.doc

• Homework 2. Due Friday, October 9.

  From the text, problems 3.4, 3.13, 3.22, 3.31, 3.32, 3.33, 3.47, 3.50, 3.71 (acd), 3.74,3.75, 3.82, 3.83, 3.85.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw2soln.pdf

• Homework 3. Due Wednesday, October 21.

  From the text, problems 4.6, 4.7, 4.10, 4.19, 4.33, 4.41, 4.48, 4.49, 4.62, 4.73, 4.77, 4.78.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw3soln.pdf

• Midterm exam solutions are available at http://www.stat.osu.edu/~snm/420/mid1soln.pdf

• Homework 4. Due Friday, October 30.

  From the text, problems 5.40, 5.41, 5.42a, 5.49, 5.51, 5.57, 5.58, 5.61, 5.64, 5.65, 5.73, 5.75, 5.78, 5.83.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw4soln.pdf

• Homework 5. Due Friday, November 6.

  From the text, problems 6.51, 6.52, 6.54, 6.55, 6.59, 6.60, 6.63, 6.66, 6.70, 6.71, 6.78, 6.79, 6.80.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw5soln.pdf

• Homework 6. Due Monday, November 16.

  From the text, problems 7.3, 7.9, 7.16, 7.18, 7.21, 7.24, 7.30, 7.47, 7.51, 7.52, 7.58, 7.65.

• Solutions are available at http://www.stat.osu.edu/~snm/420/hw6soln.pdf

• Homework 7. Due Friday, December 4.

  From the text, problems 8.61, 8.64, 8.65, 8.68, 8.73, 8.76, 8.77, 8.78, 8.79, 8.91.