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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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