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The focus of this course is to introduce students to probability and random variables. In this course, topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered in this course are uniform, exponential, normal, gamma and beta distributions, conditional probability, and Bayes theorem. Along with these joint distributions, Chebyshev inequality, law of large numbers, and central limit theorem.

### Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

### Certification

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Course Credit: MIT

### Course Curriculum

 Module: 01 Permutations and Combinations 00:35:00 Multinomial Coefficients and More Counting 00:30:00 Sample Spaces and Set Theory 00:30:00 Axioms of Probability 00:30:00 Probability and Equal Likelihood 00:25:00 Conditional Probabilities 00:20:00 Bayes’ Formula and Independent Events 00:25:00 Discrete Random Variables 00:25:00 Expectations of Discrete Random Variables 00:30:00 Variance 00:30:00 Module: 02 Binomial Random Variables, Repeated Trials and the so-called Modern Portfolio Theory 00:30:00 Poisson Random Variables 00:25:00 Poisson Processes 00:30:00 More Discrete Random Variables 00:25:00 Continuous Random Variables 00:30:00 Review for Midterm Exam 1 00:50:00 Uniform Random Variables 00:30:00 Normal Random Variables 00:25:00 Exponential Random Variables 00:30:00 More Continuous Random Variables 00:30:00 Module: 03 Joint Distribution Functions 00:30:00 Sums of Independent Random Variables 00:15:00 Expectation of Sums 00:25:00 Covariance and Correlation 00:30:00 Conditional Expectation 00:30:00 Moment Generating Distributions 00:30:00 Review for Midterm Exam 2 01:00:00 Weak Law of Large Numbers 00:20:00 Central Limit Theorem 00:30:00 Strong Law of Large Numbers and Jensen’s Inequality 00:30:00 Module: 04 Markov Chains 00:30:00 Entropy 00:30:00 Martingales and the Optional Stopping Time Theorem 00:30:00 Risk Neutral Probability and Black-Scholes 00:30:00 Review for Final Exam 00:15:00 Review for Final Exam (cont.) 00:15:00 Review for Final Exam 2 (cont.) 00:20:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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