Probability

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• Lecture Notes,  Tutorials and  Homework Assignments
  
  
• ☘  Lecture No 1:  Basic Concepts  
•         Probability vs statistics. Basic definitions. Algebra of events. Three approaches to probability.
•         Lecture              Tutorial (2024)            Solutions (2024)     
  
  
• ☘  Lecture No 2:   Conditional Probability
•        Conditional probability. Independent events. Total probability. Bayes' theorem.
•         Lecture              Tutorial (2024)            Solutions (2024)     
  
  
• ☘  Lecture No 3:   Combinatorics
•        Factorial and Gamma function. Multiplication rules. Linear and circular permutations.
         Sampling. Newton binomial and multinomial formulae.
•         Lecture              Tutorial            Solutions     
  
  
• ☘  Lecture No 4:   Univariate Discrete Random Variable
•        Basic definitions. Probability function and cumulative distribution function.
         Mean, variance, and standard deviation.
•         Lecture              Tutorial            Solutions     
  
  
• ☘  Lecture No 5:  Discrete Probability Distributions
•        Uniform, Bernoulli, binomial, geometric, negative binomial, hypergeometric,
         negative hypergeometric and Poisson distributions. Stirling formula.
         Asymptotic reductions of distributions.
•         Lecture              Tutorial            Solutions     
  
  
• ☘  Lecture No 6:  Bivariate Discrete Random Variable
•        Joint probability function, marginal probability function. Independent and correlated
         random variables, covariance and correlation coefficient. Linear regression.
•         Lecture              Tutorial            Solutions     
  
  
• ☘  Lecture No 7:  Univariate Continuous Random Variable
•         Probability density function and cumulative distribution function. Mean and variance.
         Uniform, normal, exponential and Erlang distributions.
•         Lecture              Tutorial            Solutions     
  
  
• ☘  Lecture No 8:  Central Limit Theorem
•         De Moivre—Laplace theorem, central limit theorem, and weak law of large numbers.
•         Lecture          Tutorial          Homework          Homework solutions 
  
  
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• Midterm Exams
  
  
• ☘  2019
•         MAY-24-2019          JAN-06-2019 
  
  
• ☘  2018
•         APR-20-2018          APR-15-2018 
  
  
• ☘  2017
•         DEC-03-2017 
  
  
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• Final Exams
  
  
• ☘  2022
•         FEB-20-2022             JAN-24-2022    
  
  
• ☘  2021
•         NOV-08-2021             OCT-06-2021             MAR-16-2021    
          FEB-10-2021    
  
  
• ☘  2020
•         OCT-11-2020             AUG-12-2020             JUL-03-2020    
          JUN-01-2020             APR-30-2020             FEB-28-2020    
  
  
• ☘  2019
•         JUL-18-2019          JUN-21-2019          MAR-14-2019 
          FEB-17-2019 
  
  
• ☘  2018
•         JUL-18-2018          JUN-17-2018          MAR-15-2018 
          FEB-08-2018 
  
  
• ☘  2017
•         NOV-02-2017          OCT-02-2017          JUL-27-2017 
          JUN-30-2017          MAR-27-2017          FEB-22-2017 
  
  
• ☘  2016
•         AUG-02-2016          JUN-27-2016          FEB-09-2016 
  
  
• ☘  2015
•         MAR-08-2015          FEB-05-2015 
  
  
• ☘  2014
•         JUL-24-2014          JUN-17-2014          JAN-26-2014 
  
  
• ☘  2013
•         OCT-27-2013          SEP-29-2013          AUG-27-2013 
          JUL-11-2013          MAR-03-2013          JAN-29-2013 
  
  
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• Quizzes
  
  
• ☘  2021/1:  Gap distribution in random arrangements around a circular table .
•                             Solution: JAN-20-2022
  
• ☘  2020/1:  Random chase on polygon vertices .
•                             Solution: DEC-29-2020
  
• ☘  2019/1:  How to become a millionaire .
  
•                             Background material: "The man who won the lottery 14 times"
                              Solution: MAY-14-2019
  
• ☘  2018/2:  Coin tossing can be nontrivial .
                              Solution: TBA
  
• ☘  2018/1:  Students' intra-group dynamics .
                              Solution: JUN-02-2018
  
• ☘  2017/1:  Water flow through random pipes .
                              Solution: DEC-29-2017
  
  
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