M362K: Probability 1
Course information:
Textbook:
Prerequisite and degree relevance:

M408D with a grade of at least C. A student may not receive credit for M316 after completing M362K with a grade of C or better.
Course description:

This is an introductory course in the mathematical theory of probability, thus it is fundamental to further work in probability and statistics. Principles of set theory and a set of axioms for probability are used to derive some probability density and/or distribution functions. Special counting techniques are developed to handle some problems. Properties associated with a random variable are developed for the usual elementary distributions. Both theorem proving and problem solving are required.
Course content:

Basic combinatorics: Counting principle, permutations, combinations. Basic concepts: Sample spaces, events, basic axioms and theorems of probability, finite sample spaces with equally likely probabilities. Conditional probability: Reduced sample space, independence, Bayes' Theorem. Random variables: Discrete and continuous random variables, discrete probability functions and continuous probability density functions, distribution functions, expectation, variance, functions of random variables. Special distributions: Bernoulli, Binomial, Poisson, and Geometric discrete random variables. Uniform, Normal, and Exponential continuous random variables. Approximation of Binomial by Poisson or Normal. Jointly distributed random variables: Joint distribution functions, independence, conditional distributions, expectation, covariance Sums of independent random variables: expectation, variance. Inequalities and Limit theorems: Markov's and Chebyshev's inequalities, Weak and Strong Law of Large Numbers, Central Limit Theorem.

Week
 Mon
 Wed
 Fri
1 Jan 15

1.2
2 Jan 22
 1.3
 1.4
 2.2
3 Jan 29
 2.3/2.4
 2.4/2/5
 2.5
4 Feb 5
 3.2
 3.3
 3.3
5 Feb 12
 Review
 Midterm 1
 3.4
6 Feb 19
 3.4
 4.1/4.2
 4.2/4.3
7 Feb 26
 4.4
 4.5
 4.6
8 Mar 5
 4.7
 4.8
 5.1
9 Mar 12
 spring break

10 Mar 19
 5.2
 5.3
 5.4
11 Mar 26
 Review
 Midterm 2
 5.5
12 Apr 2
 5.5
 5.6
 5.7
13 Apr 9
 6.1
 6.2
 6.3
14 Apr 16
 6.4/6.5
 7.1/7.2
 7.2/73
15 Apr 23
 8.1
 8.2
 8.3/8.4
16 Apr 30
 Review
 Midterm 3
 Review
Grading:

Late homework will not be accepted. Your two lowest homework grades will be dropped. There will be no make-up exams unless in some emergent situation.
Homeworks:


 Assignment
 Due date
 Total score
HW1
 Chapter 1, Problems 1,3,5,7,11,15,21,24
 Jan 31 before lecture
 15
HW2
 Chapter 2, Problems 1,3,7,8,9,12,15,18,23,24
 Feb 7 before lecture
 35
HW3
 Chapter 2, Problems 28,29,32,38,47,48
Chapter 3, Problems 1,4,6,10,17,19
 Feb 14 before lecture
 30
HW4
 Chapter 3, Problems 23,29,37,42,50,51,55,64,73,77
 Feb 28 before lecture
 26
HW5
 Chapter 4, Problems 1,4,7,8,14,17,19,28,33,35,38
 Mar 7 before lecture
 75
HW6
 Chapter 4, Problems 43,48,51,58,59,60,63,66,72,73,78
 Mar 21 before lecture
 31
HW7
 Chapter 5, Problems 1,3,5,6,11,15,18
 Mar 28 before lecture
 16
HW8
 Chapter 5, Problems 20,24,27,29,31,32,37,39,40
 Apr 11 before lecture
 14
HW9
 Chapter 6, Problems 2,7,8,9,10,13,16,22,24,28
 Apr 18 before lecture
 28
HW10
 Chapter 6, Problems 34,39,42
Chapter 7, Problems 4,5,7,8,11,12,14,16		 Apr 25 before lecture
HW11
 Chapter 7, Problems 21,22,30,31,37,38,39
Chapter 8, Problems 1,4,5
 May 2 before lecture

Notes:
Disabilities:

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.
Policy on scholastic dishonesty:

Students who violate university rules on scholastic dishonesty are subject to disciplinary penalties, including the possibility of failing in the course and/or dismissal from the University. Since such dishonesty harms the individual, all students, and the integrity of the University, policies on scholastic dishonesty will be strictly enforced. For further infomation, please visit the Student Judicial Services web site at http://deanofstudents.utexas.edu/.