MA222 Probability and Statistics


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

Teaching Assistant: Anton Molyboha
E-mail: Anton.Molyboha@stevens.edu
Office Hours: by appointment

Lectures:

Monday 10:00-10:50 am, Pierce 116
Wednesday 10:00-10:50 am, Peirce 116

Recitations :

Section A : Thursday 10:00-10:50 am, Pierce 120
Section B : Friday 10:00-10:50 am, E.A. Stevens 231
Section C : Tuesday 10:00-10:50 am, Pierce 120

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

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:

MA222 is a standard undergraduate course in probability and statistics for undergraduate students in sciences and engineering. This course covers 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 on recitations. There will be midterm and final exams.

Course program:

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

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

Homework 1.pdf Quiz 1.pdf

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

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

Homework 2.pdf Homework solutions 1.pdf Quiz 2.pdf

Lecture 5. - Conditional probability and independence

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

Quiz 2 solution.pdf

Lecture 6. - Random variables

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

Homework 3.pdf Homework solutions 2.pdf Quiz 3.pdf

Lecture 7. - Joint probability distributions, statistical independence

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

Quiz 3 solution.pdf

Lecture 8. - Review and exercises

Homework 4.pdf Homework solutions 3.pdf Quiz 4.pdf

Lecture 9. - Review and exercises

Lecture 10. - Mathematical expectation

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

Lecture 11. - Covariance

11.1. Covariance
11.2. Correlation coefficient

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

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

Lecture 14. - Chebyshev's Theorem

14.1. Chebyshev's Theorem
14.2. Review and exercises

Lecture 15. - Discrete probability distributions 1

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

Lecture 16. - Discrete probability distributions 2

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

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

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

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

Lecture 20. - Fundamental sampling distributions 2

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

Lecture 21. - Single sample

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

Lecture 22. - Two samples

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

Lecture 23. - Estimating the variance

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

Lecture 24. - Statistical hypotheses 1

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

Lecture 25. - Statistical hypotheses 2

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

Lecture 26. - Review and exercises

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