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ABET Course Objectives and Outcomes Form

Course number and title: EE131A Probability
Credits: 4
Instructor(s)-in-charge: L. Dolecek (dolecek@ee.ucla.edu)
  K. Yao (yao@ee.ucla.edu)
Course type: Lecture
Required or Elective: Required.
Course Schedule:
Lecture: 4 hrs/week. Meets twice weekly.
Dicussion: 1 hr/discussion section. Multiple discussion sections offered per quarter.
Outside Study: 10 hrs/week.
Office Hours: 2 hrs/week by instructor. 2 hrs/week by each teaching assistant.
 
Course Assessment:
Homework: 8 assignments.
Exams: 1 midterm and 1 final.
Design: Matlab-based design project.
 
Grading Policy: Typically 20% homework, 10% design, 30% midterm, 40% final.
Course Prerequisites: EE102, Math 32B, and Math 33B.
Catalog Description: Introduction to basic concepts of probability, including random variables and vectors, distributions and densities, moments, characteristic functions, and limit theorems. Applications to communication, control, and signal processing. Introduction to computer simulation and generation of random events.  
Textbook and any related course material:
¤ A. Leon-Garcia, Probability and Random Processes for Electrical Engineers, 2nd edition, Addison Wesley, 1993.
 
Course Website
Additional Course Website
Topics covered in the course and level of coverage:
¤ Introduction to probability models in electrical engineering. 2 hrs.
¤ Basic axioms of probability, sample space, events, conditional probability. 2 hrs.
¤ Computing probabilities using counting. 4 hrs.
¤ Dependence and Independence of events and sequential experiments. 2 hrs.
¤ Random variables, density functions, cumulative distribution functions, characteristic functions. 3 hrs.
¤ Important discrete and continuous random variables, functions of random variables. 6 hrs.
¤ Two-dimensional random variables. 6 hrs.
¤ Law of large numbers and Central Limit Theorem. 3 hrs.
¤ Data fitting and computer generation of random variables. 2hrs plus outside study
Course objectives and their relation to the Program Educational Objectives:  
Contribution of the course to the Professional Component:
Engineering Topics: 0 %
General Education: 0 %
Mathematics & Basic Sciences: 0 %
Expected level of proficiency from students entering the course:
Mathematics: Strong
Physics: Not Applicable
Chemistry: Not Applicable
Technical writing: Average
Computer Programming: Average
Material available to students and department at end of course:
  Available to
students
Available to
department
Available to
instructor
Available to
TA(s)
Course Objectives and Outcomes Form: X X X X
Lecture notes, homework assignments, and solutions: X X X X
Samples of homework solutions from 2 students: X
Samples of exam solutions from 2 students: X
Course performance form from student surveys: X X
Will this course involve computer assignments? YES Will this course have TA(s) when it is offered? YES

  Level of contribution of course to Program Outcomes
(a) Strong  
(b) Strong  
(c) Strong  
(g) Average  
(i) Average  
(l) Strong  
(m) Average  
(n) Strong  
Strong: (a) (b) (c) (l) (n)
Average: (g) (i) (m)

:: Upon completion of this course, students will have had an opportunity to learn about the following ::
  Specific Course Outcomes Program Outcomes
1. Construct sample spaces of random experiments; identify and specify events, and perform set operations on events. a c i l
2. Motivate and understand the axioms of Probability from frequency of occurrence perspectives. a i l m
3. Construct simple Probability measures for discrete and random sample spaces; e.g., uniform distributions over sample spaces. a l
4. Compute probabilities by counting; Learn to be able to count permutations and combinations of n objects. a l m n
5. Compute conditional probability of events, and determine dependence/independence of events. a l m
6. Use Baye�s law to compute �a posteriori� probabilities of events. a l
7. Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels. a b c i l
8. Obtain random variables corresponding to random experiments; Specify probability density and cumulative distribution functions for both discrete and continuous random variables. Calculate the distributions for functions of random variables. a l m
9. Compute the expected value, variance, and higher-order moments of random variables (for both discrete and continuous types). a l m
10. Use standard discrete random variables used in science and engineering, including Bernoulli, binomial, multinomial, geometric, and Poisson random variables. Learn elementary applications to traffic modeling. a l m n
11. Use standard continuous random variables used in science and engineering, including , exponential, Gaussian, Cauchy, and Gamma, distributions. Learn elementary applications to noise modeling. a l m
12. Use Markov and Chebyshev inequalities to obtain bounds on probability of events. a l m
13. Use characteristic functions of random variables to compute (I) distributions of sums of independent random variables, and (ii) moments of random variables. a l m
14. Usel 2-dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2-d random variables. Compute marginal and conditional distributions of random variables. a l m
15. Use law of large numbers to determine convergence of sample estimates to true parameters. a i l
16. Use the central limit theorem to compute probabilities. a i l
17. Use of chi-square test to determine the goodness of the fit of a distribution to data. a b l m
18. Use deterministic algorithms (that can be implemented on computers) to generate pseudo-random numbers. a b l n
19. Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlab-based design project requiring some independent reading, programming, simulations and technical writing. b c g i
20. Opportunities to interact weekly with the instructor and the teaching assistant(s) during regular office hours and discussion sections in order to further the students' learning experience and the students' interest in the material. i

  Program outcomes and how they are covered by the specific course outcomes
(a) ¤  Construct sample spaces of random experiments; identify and specify events, and perform set operations on events.  
¤  Motivate and understand the axioms of Probability from frequency of occurrence perspectives.  
¤  Construct simple Probability measures for discrete and random sample spaces; e.g., uniform distributions over sample spaces.  
¤  Compute probabilities by counting; Learn to be able to count permutations and combinations of n objects.  
¤  Compute conditional probability of events, and determine dependence/independence of events.  
¤  Use Baye�s law to compute �a posteriori� probabilities of events.  
¤  Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels.  
¤  Obtain random variables corresponding to random experiments; Specify probability density and cumulative distribution functions for both discrete and continuous random variables. Calculate the distributions for functions of random variables.  
¤  Compute the expected value, variance, and higher-order moments of random variables (for both discrete and continuous types).  
¤  Use standard discrete random variables used in science and engineering, including Bernoulli, binomial, multinomial, geometric, and Poisson random variables. Learn elementary applications to traffic modeling.  
¤  Use standard continuous random variables used in science and engineering, including , exponential, Gaussian, Cauchy, and Gamma, distributions. Learn elementary applications to noise modeling.  
¤  Use Markov and Chebyshev inequalities to obtain bounds on probability of events.  
¤  Use characteristic functions of random variables to compute (I) distributions of sums of independent random variables, and (ii) moments of random variables.  
¤  Usel 2-dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2-d random variables. Compute marginal and conditional distributions of random variables.  
¤  Use law of large numbers to determine convergence of sample estimates to true parameters.  
¤  Use the central limit theorem to compute probabilities.  
¤  Use of chi-square test to determine the goodness of the fit of a distribution to data.  
¤  Use deterministic algorithms (that can be implemented on computers) to generate pseudo-random numbers.  
(b) ¤  Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels.  
¤  Use of chi-square test to determine the goodness of the fit of a distribution to data.  
¤  Use deterministic algorithms (that can be implemented on computers) to generate pseudo-random numbers.  
¤  Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlab-based design project requiring some independent reading, programming, simulations and technical writing.  
(c) ¤  Construct sample spaces of random experiments; identify and specify events, and perform set operations on events.  
¤  Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels.  
¤  Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlab-based design project requiring some independent reading, programming, simulations and technical writing.  
(g) ¤  Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlab-based design project requiring some independent reading, programming, simulations and technical writing.  
(i) ¤  Construct sample spaces of random experiments; identify and specify events, and perform set operations on events.  
¤  Motivate and understand the axioms of Probability from frequency of occurrence perspectives.  
¤  Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels.  
¤  Use law of large numbers to determine convergence of sample estimates to true parameters.  
¤  Use the central limit theorem to compute probabilities.  
¤  Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlab-based design project requiring some independent reading, programming, simulations and technical writing.  
¤  Opportunities to interact weekly with the instructor and the teaching assistant(s) during regular office hours and discussion sections in order to further the students' learning experience and the students' interest in the material.  
(l) ¤  Construct sample spaces of random experiments; identify and specify events, and perform set operations on events.  
¤  Motivate and understand the axioms of Probability from frequency of occurrence perspectives.  
¤  Construct simple Probability measures for discrete and random sample spaces; e.g., uniform distributions over sample spaces.  
¤  Compute probabilities by counting; Learn to be able to count permutations and combinations of n objects.  
¤  Compute conditional probability of events, and determine dependence/independence of events.  
¤  Use Baye�s law to compute �a posteriori� probabilities of events.  
¤  Use probability models to calculate (I) the odds of winning/losing in card and other games that involve random experiments, (ii) errors in binary communication channels, and (iii) Bayesian inference of symbols sent over noisy communication channels.  
¤  Obtain random variables corresponding to random experiments; Specify probability density and cumulative distribution functions for both discrete and continuous random variables. Calculate the distributions for functions of random variables.  
¤  Compute the expected value, variance, and higher-order moments of random variables (for both discrete and continuous types).  
¤  Use standard discrete random variables used in science and engineering, including Bernoulli, binomial, multinomial, geometric, and Poisson random variables. Learn elementary applications to traffic modeling.  
¤  Use standard continuous random variables used in science and engineering, including , exponential, Gaussian, Cauchy, and Gamma, distributions. Learn elementary applications to noise modeling.  
¤  Use Markov and Chebyshev inequalities to obtain bounds on probability of events.  
¤  Use characteristic functions of random variables to compute (I) distributions of sums of independent random variables, and (ii) moments of random variables.  
¤  Usel 2-dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2-d random variables. Compute marginal and conditional distributions of random variables.  
¤  Use law of large numbers to determine convergence of sample estimates to true parameters.  
¤  Use the central limit theorem to compute probabilities.  
¤  Use of chi-square test to determine the goodness of the fit of a distribution to data.  
¤  Use deterministic algorithms (that can be implemented on computers) to generate pseudo-random numbers.  
(m) ¤  Motivate and understand the axioms of Probability from frequency of occurrence perspectives.  
¤  Compute probabilities by counting; Learn to be able to count permutations and combinations of n objects.  
¤  Compute conditional probability of events, and determine dependence/independence of events.  
¤  Obtain random variables corresponding to random experiments; Specify probability density and cumulative distribution functions for both discrete and continuous random variables. Calculate the distributions for functions of random variables.  
¤  Compute the expected value, variance, and higher-order moments of random variables (for both discrete and continuous types).  
¤  Use standard discrete random variables used in science and engineering, including Bernoulli, binomial, multinomial, geometric, and Poisson random variables. Learn elementary applications to traffic modeling.  
¤  Use standard continuous random variables used in science and engineering, including , exponential, Gaussian, Cauchy, and Gamma, distributions. Learn elementary applications to noise modeling.  
¤  Use Markov and Chebyshev inequalities to obtain bounds on probability of events.  
¤  Use characteristic functions of random variables to compute (I) distributions of sums of independent random variables, and (ii) moments of random variables.  
¤  Usel 2-dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2-d random variables. Compute marginal and conditional distributions of random variables.  
¤  Use of chi-square test to determine the goodness of the fit of a distribution to data.  
(n) ¤  Compute probabilities by counting; Learn to be able to count permutations and combinations of n objects.  
¤  Use standard discrete random variables used in science and engineering, including Bernoulli, binomial, multinomial, geometric, and Poisson random variables. Learn elementary applications to traffic modeling.  
¤  Use deterministic algorithms (that can be implemented on computers) to generate pseudo-random numbers.  

:: Last modified: February 2013 by J. Lin ::

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