University of California, Irvine (UCI)
School of Information and Computer Sciences (ICS)
Institute for Genomics and Bioinformatics (IGB)

Introduction to Probability and Statistics

ICS/Math 67
Pierre Baldi



Organization - Functioning - Policies - Topics - Homeworks



Pierre Baldi

Teaching Assistants

Office Hours

Pierre Baldi: by appointment [ICS 424, C]

Lectures and discussion sections

Lectures: Mo We 2:00-3:20 in  IERF B015

Instruction begins on Friday Jan 3.
Instruction ends on Friday March 14.

No classes on Monday Jan 20 and Monday  Feb 17.



Organization - Functioning - Policies - Topics - Homeworks



There is one required textbook for the course:

A First Course in Probability

Sixth Edition,  by Sheldon Ross (Prentice Hall 2002).

The textbook explains the subject material in detail. It is strongly recommended that you read the book and attend all lectures and all meetings of your discussion section. You will be responsible for all material covered in the lectures and discussion sections, and for all assigned reading in the book.

Course Grades

There will be 7-8 homeworks , one midterm and one final.. Homework will be assigned each Wednesday and will be due the following week.  The weighting scheme for the final grade is:

Homework assignments 15%
Midterm 35%
Final 50%

We will drop the two lowest homework scores in determining your final grade. The midterm exam will be given in lecture. It is scheduled for Wednesday, February 12. The final examination is scheduled for TBA.

A work-related conflict is NOT a valid reason for postponing an exam. The dates of the exams are being announced now. Plan accordingly.

Please bring your student ID to all exams.

Obtaining Assistance

The best way to get your questions answered is by coming to lecture, section or office hours and asking them there.

Any student who feels he or she may need an accommodation based on  the impact of a disability should contact me privately to discuss his or her specific needs. Also contact the Disability Services Center at (949) 824-7494 as soon as possible to better ensure that such accommodations are implemented in a timely fashion.


Class announcements will be made in lecture and in section. Important announcements will also be posted on the class Web page.

Homework and Handouts

The homework assignments will be handed out at the beginning of lectures and posted on the Web.

The homework problems are an integral part of the course. They complement the material covered in the lectures by providing examples, applications, and extensions. You are strongly encouraged to attempt all problems. Even if you cannot solve them, if you have tried hard to solve them you may be more likely to understand and remember the solution. Our brains learn something while attempting to solve a problem, even (and perhaps especially) during failed attempts. So do not get discouraged if a problem is difficult.

Discussion Section

You must be registered for a discussion section. The discussion section provides you with an opportunity to ask questions about the lecture material. It is strongly recommended that you attend a discussion section regularly. You are responsible for all material covered there.


Organization - Functioning - Policies - Topics - Homeworks

Course Policies

Late Assignments

Homework assignments are due every Wednesday by 2:00 PM. Absolutely no homework assignments will be accepted after 2:000 PM. If your homework is not turned by then, you will receive a 0.


Only parts of the homework assignments will be graded. However, you will not know which particular problems will be graded before you hand in your assignment. All the problems in the midterm and the final will be graded.

Questions on Grading

Any questions regarding grading should be directed to your TA first and then to me during office hours or before or at the end of the lectures.


You are allowed, and even encouraged, to discuss the solutions to the homework with your fellow classmates. However, you are required to sit down and write up your own solutions independently. In addition, you need to write down the names of any classmates with whom you have collaborated on a given assignment, clearly indicating that they are your collaborators. Copying the homework assignment of another student is considered cheating. Keep in mind that the homework contributes little to your final grade in comparison to the midterm and the final. Thus, it is very much in your own best interest to have a thorough understanding of the homework assignments.

Academic Honesty

Cheating on any kind of in class examination will be taken very seriously. Any such incident will result in a letter describing the incident which is placed in your file on campus. Depending on the severity of the incident, the resulting grade can range from an F on the particular examination to an automatic F in the course. Additional penalties may also be imposed by the department and the university. Very severe incidents of academic dishonesty can result in suspension or expulsion from the university.

ICS Change of Grade Option Policy

The ICS departmental deadline for any ICS major to change their grade option is the end of 6th week with instructor's approval. Dean's signature (available at the ICS Student Affairs office) will be required after the deadline and the ICS Student Affairs office does not allow a change of grade option for any course after 6th week, unless the student has documented a medical or financial hardship.

ICS Add Deadline

The ICS departmental deadline for any ICS major to add an ICS course is the end of 3rd week with instructor's approval. Any course additions after the 3rd week of classes requires Dean's signature and careful review by the ICS Student Affairs office. If you are adding a course after the 3rd week, please go to the ICS Student Affairs office.


Organization - Functioning - Policies - Topics - Homeworks

List of Topics

bullet Week 1:Introduction. Combinatorics and Counting. Axioms of Probability. Frequentist and Degree of Belief Approaches.
bullet Week 2: Combinatorics and Counting. Conditional Probability and Independence. Bayes theorem. Introduction to Discrete Random Variables. Expectation. Variance.
bullet Week 3: Combinatorics and Counting. Discrete Random Variables.  Binomial, Geometric, Poisson .
bullet Week 4: Markov Chains. Continuous Random Variables. Uniform, Gaussian, Exponential, Gamma, Beta.
bullet Week 5: Z-scores. Jointly Distributed Random Variables.
bullet Week 6:  Review. Midterm.
bullet Week 7: Simulations and Random Sampling. Monte Carlo Methods.
bullet Week 8: Basic Concepts in Statistics: From Data to Hypothesis and Models. Bayesian Framework.
bullet Week 9: Dice Models. Decision Making. T-test.
bullet Week 10:   Introduction to Linear and Non-linear Regression and Classification.
bullet Week 11: Final exam.


Organization - Functioning - Policies - Topics - Homeworks


Due by January 15:
p. 53: 1, 3, 5, 10, 17, 23, 24, 36, 46, 55

Due by January 22:
p. 104: 1, 5, 13, 16, 21, 24, 33, 40, 49, 50, 53, 56, 65, 69, 85

Due by January 29:
p. 171: 2, 13, 20, 27, 30, 41, 43, 48, 51, 52, 54, 58, 61, 70

Due by February 5:
p. 228: 1 , 4, 6, 7, 8, 11, 14, 15, 16, 17,18, 19, 20, 21, 23, 24, 26, 27, 28, 29.

Due by February 19:
p. 228: 32,3 4, 39, 40

A coin is flipped 1,000 time s and 700 heads are observed. Using a simple family of models parameterized by p (the probability of heads on a single toss) derive the Maximum Likelihood estimate of p. Using a Beta prior on p, with parameters a and b, derive the Maximum A Posteriori Estimate of p. What happens if the prior is uniform? What if a=b=5? In both cases, plot the prior and posterior densities.

Due by February 26:
You are interested in estimating the number of email messages received by the UCI campus in one day (email addresses ending in ""). Prior to seeing any data, provide a reasonable guess and standard deviation for your estimate. Imagine that on two different days, the actual number of messages is: 210,000 and 220,000. How would this change your estimate and why? Build a Maximum Likelihood and Maximum A Posteriori framework for your answers.

Due by March 5:
p. 471: 2, 3

Write and run a computer program to estimate the area between a normal density function and the x-axis, from minus one to plus one standard deviation from the mean, by simulating a sequence of Bernoulli trials.
p. 290: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Due by March 12:

  1. Let X and Y be two 0-1 variables with P(0,0)=0.1, P(0,1)= 0.1, P(1,0)=0.2, P(1,1)=0.6. Computer the marginal probabilities of X and Y. Are X and Y independent? Computer the Covariance and the Correlation Coefficient between X and Y.
  2. A webmaster of a particular web site is interested in studying the relationship between the indegree X of a web page and the number Y of its visitors per day. After monitoring the web site for a few days he finds the following average values:
    X=2 Y= 21; X=3 Y=33; X=5 Y= 55, X=10 Y=99, X=20 Y= 220

Estimate the number of daily visitors to a web page with indegree: (a) 15; (b) 30. Explain.

Solution to Midterm


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© 2017 Pierre Baldi | pfbaldi [at] uci [dot] edu