This course is offered to engineering students (excluding electrical engineering students) and covers the following topics:
Part 1:
- Concepts of random experiments, sample spaces, and events
- Probability function
- Calculation of probabilities in finite equally likely and non-equally likely sample spaces
- Calculation of probabilities in infinite countable and continuous sample spaces
- Conditional probability
- Bayes theorem
- Law of total probability
Part 2:
- The concept of a random variable
- Discrete and continuous probability distributions
- Bivariate and multivariate probability distributions
Part 3:
- Concept and definition of expected value
- Expected value of functions of random variables
- Rules of expected value
- Variance and covariance
- Conditional expected value and conditional variance
Part 4:
- Important discrete probability distributions, such as the Bernoulli, binomial, Poisson, and hypergeometric distributions, etc.
- Important continuous probability distributions, such as the exponential, normal, and continuous uniform distributions, etc.
Part 5:
- Introduction to statistical inference
- Parameter estimation for a single population (population mean and population variance)
- Parameter estimation for two populations (difference between two population means and ratio of two population variances)
Part 6:
- Basic concepts of hypothesis testing
- Statistical hypothesis testing for population parameters
- Goodness-of-fit tests
