Stochastic Process - Computational Statistics and Probability Quiz
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Questions and Answers

What is a stochastic process?

  • A sequence of random numbers with fixed values at different points of time.
  • A set of deterministic variables where X(t) takes the same value at different points of time.
  • A set of random variables with fixed values at different points of time.
  • A family of random variables where X(t) takes different values at different points of time. (correct)

    • What defines a discrete-time process?

  • The set T being finite or countable. (correct)
  • The set T being infinite and uncountable.
  • The set T being continuous.
  • The set T being a subset of real numbers.

    • What characterizes a continuous-time process?

  • T being a subset of real numbers.
  • T not being finite or countable. (correct)
  • T being an infinite sequence.
  • T being finite and countable.

    • What is the state space in a stochastic process?

    <p>The set of real values that X(t) can take.</p> Signup and view all the answers

    What does a continuous-time process have for every instant in time?

    <p>A value of X(t) defined for every instant t.</p> Signup and view all the answers

    What characterizes a continuous-time process?

    <p>It has a non-finite or non-countable set for time, such as $T = [0,\infty)$</p> Signup and view all the answers

    What defines a discrete-time process?

    <p>It has a finite or countable set for time, such as $T = {0, 1, 2, 3, ...}$</p> Signup and view all the answers

    What does a stochastic process consist of?

    <p>A family of random variables ${X(t) : t \in T}$</p> Signup and view all the answers

    What is the state space in a stochastic process?

    <p>The set of real values that $X(t)$ can take</p> Signup and view all the answers

    What does a continuous-time process have for every instant in time?

    <p>$X(t)$ associated with every instant in time</p> Signup and view all the answers

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