MA118 Probability for Business and Liberal Arts


Instructor: Nikolay Strigul
E-mails: nstrigul@stevens.edu, nstrigul@princeton.edu
Office Hours: by appointment

Grader: Vitalii Kushnirenko
E-mail: Vitallii.Kushirenko@stevens.edu
Office Hours: by appointment

Lectures:

Monday 1:00-1:50 pm, Kidde 228
Wednesday 12:00-12:50 pm, Peirce 120

Practicums :

Section A : Friday 10:00-10:50 am, Peirce 220.
Section B : Friday 1:00-1:50 pm, Peirce 220.
Section C : Friday 2:00-2:50 pm, Peirce 220.

Homework: There will be weekly homework assignments.
Exams: There will be midterm and final exams.
Quizzes: Every practicum will start with a closed book quiz covering definitions and theorems.

Grading: Textbook: Probability & Statistics for Engineers & Scientists by R.E. Walpole, R.H. Myers, S.L. Myers, K. Ye, ISBN: 0131877119

Course program Course program (PDF)

General comments:

MA118 is an undergraduate course in probability and statistics, designed for undergraduate students in Business and Liberal Arts. It introduces basic concepts and methods in probability and statistics such as sample space, discrete and continuous random variables, probability distributions, introduction to the statistical inference, estimation, and testing statistical hypotheses. Students will have weekly homework assignments and closed book quizzes covering definitions, major theorems and previous homework problems. There will be midterm and final exams. In addition to the lectures, students will watch an on-line educational series on statistics developed by the Annenberg Channel. This series is a bit old (produced in 1989), but is an excellent and extremely useful series that introduces the basic ideas of probability and statistics through real-life examples. Watching the programs that correspond to the current material is a mandatory homework assignment. I hope that these video lectures will stimulate student interest in probability and statistics, and save lecture time for theory and examples. This on-line video series is located at the Annenberg Media website:

http://www.learner.org/resources/series65.html

These programs can be viewed free of charge, after free registration at

http://www.learner.org/vod/form.html

Course program:

Jan 17. Lecture 1. - Introduction to statistics and data analysis

1.1. Sampling procedures
1.2. Measures of location: the sample mean
1.3. Measures of variability
1.4. Discrete and continuous data
1.5. Graphical methods and data descriptions

Jan 22. Lecture 2. - Sample space

2.1. Sample space
2.2. Events
2.3. Complement of an event
2.4. Intersection and union of events
2.5. Disjoint events
2.6. Venn diagrams

Jan 24. Lecture 3. - Counting sample points

3.1. The multiplication rule
3.2. Permutations
3.3. Number of permutations of n distinct objects taken r at a time
3.4. Number of permutations of n things of k kinds
3.5. Number of ways of partitioning a set of n objects
3.6. Number of combinations of n distinct objects taken r at a time

Jan 29. Lecture 4. - Probability

4.1. Probability of an event
4.2. Probability and relative frequency
4.3. Additive rule for two events
4.4. Partition of sample space
4.5. Generalisation of additive rule for three events

Jan 31. Lecture 5. - Conditional probability and independence

5.1. Conditional probability
5.2. Independent events
5.3. Multiplicative rules
5.4. Bayes' formula

Feb 5. Lecture 6. - Random variables

6.1. Concept of random variable
6.2. Discrete probability distributions
6.3. Continious probability distributions

Feb 7. Lecture 7. - Joint probability distributions, statistical independence

7.1. Joint probability distributions
7.2. Marginal distributions
7.3. Conditional distributions
7.4. Statistical independence

Feb 12. Lecture 8. - Review and exercises

Feb 14. Lecture 9. - Review and exercises

Feb 20. Lecture 10. - Mathematical expectation

10.1. Mean of random variable
10.2. Variance
10.3. Standard deviation

Feb 21. Lecture 11. - Covariance

11.1. Covariance
11.2. Correlation coefficient

Feb 26. Lecture 12. - Means of linear combinations of random variables

12.1. Expected value of a linear function of a random variable
12.2. Expected value of the sum or difference of functions of a radom variable
12.3. Expected value of multiplication of two independent random variables

Feb 28. Lecture 13. - Variances of functions of random variables

13.1. Variance of a linear function of a random variable
13.2. Variance of a linear combination of two random variables
13.3. Expected value and variance of non-linear functions of a random variable
13.4. Linearization

Mar 5. Lecture 14. - Chebyshev's Theorem

14.1. Chebyshev's Theorem
14.2. Review and exercises

Mar 7. Lecture 15. - Discrete probability distributions 1

15.1. Discrete uniform distribution
15.2. The Bernoulli process
15.2. Binomial distribution

Spring recess.

Mar 19. Lecture 16. - Discrete probability distributions 2

16.1. Hypergeometric distribution
16.2. Negative binomial distribution
16.2. Poisson process

Mar 21. - Midterm exam.

Mar 26. Lecture 17. - Continuous probability distributions 1

17.1. Continuous uniform distribution
17.2. Normal distribution
17.3. Areas under the normal curve
17.4. Applications of the normal distribution

Mar 28. Lecture 18. - Continuous probability distributions 2

18.1. Gamma distribution
18.2. Exponential distribution
18.3. Applications of gamma and exponential distributions
18.4. Lognormal distribution

Apr 2. Lecture 19. - Fundamental sampling distributions 1

19.1. Random sampling
19.2. Some important statistics
19.3. Sampling distribution of means
19.4. Sampling distribution of sample variances

Apr 4. Lecture 20. - Fundamental sampling distributions 2

20.1. t-Distribution
20.2. F-Distribution
20.3. Review and exercises

Apr 9. Lecture 21. - Single sample

21.1. Estimating the mean
21.2. Standard error
21.3. Prediction intervals

Apr 11. Lecture 22. - Two samples

22.1. Estimating the difference between two means
22.2. Paired observations
22.3. Proportions

Apr 16. Lecture 23. - Estimating the variance

23.1. Single sample
23.2. Estimating the ratio of two variances
23.3. Review and exercises

Apr 18. Lecture 24. - Statistical hypotheses 1

24.1. Testing a statistical hypothesis
24.2. P-values
24.3. One- and two-tailed tests

Apr 23. Lecture 25. - Statistical hypotheses 2

25.1. Tests on a single mean
25.2. Tests on two means

Apr 25. Lecture 26. - Review and exercises

May 3 - Final exam

back