Introduction to Stochastic Processes: Key Concepts and Examples UPDATED ACTUAL Questions and CORRECT Answers

Introduction to Stochastic Processes: Key
Concepts and Examples UPDATED ACTUAL
Questions and CORRECT Answers


What is a stochastic process? A collection of random variables indexed by a set,
typically representing time.


What does the index set T represent The domain over which the process is observed,
in a stochastic process? often denoting time.


What is the state space in a The space in which the random variables take
stochastic process? values, denoted as X.


What is a sample path in the context A realization of the process, represented as xt.
of stochastic processes?


What characterizes a discrete-time The index set T consists of discrete time points, e.g.,
stochastic process? {Xt, t = 0, 1, ...}.




What characterizes a continuous- The index set T consists of a continuous range of
time stochastic process? time points, e.g., {Xt, t ∈ [0, ∞)}.