Calendar
Week 1
Lecture
Basic concepts of probability and areas of formation.
Necessary foundations include: set theory and combinatorics.
Probability space, random variables, and Kolmogorov’s principles in the discrete case.
Syllabus PDF
Week 2
Lecture
Conditional Probabilities and Bayes’ Theorem.
Conditional Independence and Markov Chain Law, Statistical Independence.
Week 3
Lecture
Repeated tests, Bernoulli trial, example solving, and review.
Probability space, random variable in continuous state.
Week 4
Lecture
Redefinition of random variables, distribution functions, and probability density functions.
Special random variables such as Gaussian, Poisson, etc.
Week 5
Lecture
Continuation of special random variables.
Statistics of a random variable: Mean, variance, etc.
Week 6
Lecture
Conditional distributions.
Functions of random variables: Distribution and probability density functions, moments, and characteristic functions.
Week 7
Lecture
Joint distribution of random variables, bivariate distribution, marginal distribution, and…
Univariate functions of two random variables.
Practical AssignmentQuestion
Week 8
Lecture
Two-dimensional functions of two random variables: Distribution function.
Central Limit Theorem.
Week 9
Lecture
Probabilistic Inequalities (Markov’s and Chebyshev’s Inequalities)
Statistical Correlation, Conditional Expectation, and Their Properties
Covariance and Its Properties
Week 10
Lecture
Introduction to Statistics, Basic Concepts, and Applications
Estimation Theory, Point and Interval Estimation
Week 11
Lecture
Continuation of Point and Interval Estimators
Maximum Likelihood Estimation (MLE)
Week 12
Lecture
Estimation of Mean Squared Error (MSE) and Confidence Intervals
Concept of Bias and Variance
Week 13
Lecture
Hypothesis Testing, Fisher Tests, t-tests, and …
Concept and Calculation of p-value