
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 Bayeï¿½s law to compute ï¿½a posterioriï¿½ 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 higherorder 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 2dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2d 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 chisquare test to determine the goodness of the fit of a distribution to data. 



¤ 
Use deterministic algorithms (that can be implemented on computers) to generate pseudorandom 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 chisquare test to determine the goodness of the fit of a distribution to data. 



¤ 
Use deterministic algorithms (that can be implemented on computers) to generate pseudorandom numbers. 



¤ 
Several homework assignments delving on core concepts and reinforcing analytical skills learned in class. Opportunity to conduct a matlabbased 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 matlabbased 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 matlabbased 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 matlabbased 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 Bayeï¿½s law to compute ï¿½a posterioriï¿½ 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 higherorder 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 2dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2d 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 chisquare test to determine the goodness of the fit of a distribution to data. 



¤ 
Use deterministic algorithms (that can be implemented on computers) to generate pseudorandom 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 higherorder 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 2dimensional random vectors to model experiments with two simultaneous outcomes. Compute the distributions of functions of 2d random variables. Compute marginal and conditional distributions of random variables. 



¤ 
Use of chisquare 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 pseudorandom numbers. 

  