Math 432: Stochastic Processes Chapter 1 Quiz

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Questions and Answers

What is the definition of a stochastic process?

  • A collection of random numbers
  • A family of random variables which are functions of time (correct)
  • A sequence of deterministic variables
  • A set of random experiments

In Example 1.1, what type of stochastic process is ሼܺ௡ ǡ ݊ ൒ ͳሽ?

  • Binomial process
  • Geometric process
  • Bernoulli process (correct)
  • Exponential process

What does ܺ௡ represent in Example 1.2?

  • The maximum outcome
  • The minimum outcome
  • The number of sixes in the first n throws (correct)
  • The sum of all outcomes

What kind of stochastic process is described in Example 1.3?

<p>Maximum process (B)</p> Signup and view all the answers

What are the outcomes of the nth throw of a die in Example 1.1 known as?

<p>Bernoulli processes (D)</p> Signup and view all the answers

What is the number of sixes in the first n throws of a die in Example 1.2 an example of?

<p>Binomial variable (C)</p> Signup and view all the answers

In the context of the given text, what is meant by X(1)?

<p>The number which appears at the first toss of the die (C)</p> Signup and view all the answers

What is the state space for the stochastic process described in the given text?

<p>The set of all values of the individual random variable (A)</p> Signup and view all the answers

According to Remark 1.1, if ܵ is discrete, what is ሼܺ ‫ ݐ‬ሽ called?

<p>Discrete state stochastic process (D)</p> Signup and view all the answers

What does X(1980) represent in the context of the given text?

<p>The number of students admitted in 1980 (B)</p> Signup and view all the answers

In Example 1.6, what does ܻሺ‫ݐ‬ሻ represent?

<p>The number of patients waiting at time ‫ݐ‬ (D)</p> Signup and view all the answers

What is meant by continuous time stochastic process according to Remark 1.2?

Signup and view all the answers

In Definition 1.3, what does T represent?

<p>The index parameter for the stochastic process ܺ ‫ݐ‬ (D)</p> Signup and view all the answers

According to Remark 1.2, what is ܺ ‫ݐ‬ called if T is continuous?

<p>Continuous time stochastic process (A)</p> Signup and view all the answers

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