The probability mass function, cumulative distribution function, expectation and variance for random variables.
We introduce the binomial (Bernoulli), geometric and Poisson probability distributions and their properties. The properties include their expectations, variances and moment generating functions.
The probability density function, cumulative distribution function, expectation and variance for a continuous random variable.
The uniform distribution, normal distribution, exponential distribution and their properties.
Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation.
Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions.
We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place.