1. the fundamental concepts of probability:
1.1. define the relevant random events of a random experiment, compute the probabilities of simple and composition of events.
1.2. check the independence of events, compute the conditional probabilities, use Bayes’ Theorem.
2. the concept of random variables and the probability distributions:
2.1. compute probabilities related to a random variable, expected value and variance of a random variable using probability mass function, probability density function, cumulative distribution function.
2.2. know and use properties of some well-known discrete and continuous probability distributions.
3. the concept of random vectors and random samples:
3.1. use joint distributions to compute probabilities of events in more than one random variable, compute marginal distributions, compute the distributions of functions of two random variables.
3.2. know properties of random samples and the distributions of the sample mean and sample variance.