Math 432: Stochastic Processes Chapter 1 Quiz

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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?

Maximum process Signup and view all the answers

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

Bernoulli processes 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?

Binomial variable Signup and view all the answers

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

The number which appears at the first toss of the die Signup and view all the answers

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

The set of all values of the individual random variable Signup and view all the answers

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

Discrete state stochastic process Signup and view all the answers

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

The number of students admitted in 1980 Signup and view all the answers

In Example 1.6, what does ܻሺ‫ݐ‬ሻ represent?

The number of patients waiting at time ‫ݐ‬ Signup and view all the answers

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

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In Definition 1.3, what does T represent?

The index parameter for the stochastic process ܺ ‫ݐ‬ Signup and view all the answers

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

Continuous time stochastic process Signup and view all the answers

Math 432: Stochastic Processes Chapter 1 Quiz

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