**Probabilistic View:** A stochastic process is a sequence (collection) of [[Random Variable|random variables]]. It is characterized by: - Properties of each individual $X_i$ (e.g. [[Expectation]], [[Variance]], [[Probability Density Function|PDF]]). - Interrelations between $X_i$ to $X_j$ within the sequence ([[Joint Probability Density Function|Joint PDF]]). - For a complete probabilistic view, we need to identify the joint PDF $f_{X_1, \dots, X_n}(x_1, \dots , x_n)$ of the full sequence (finite or infinite). **Timely View:** A stochastic process is not just a collection of r.v’s. In this view we emphasize that it is a sequence indexed e.g. by time. - The sequence captures just one possible outcome per time-unit within an experiment. - The sample space $\Omega$ is the set of all infinite sequences (e.g. of $\{0,1\}$ for a [[Bernoulli Process]]).