MathIsimple – Simple, Friendly Math Tools & Learning

Core Definition

1 questions

Question 1: Independent Increment Definition

Which of the following statements correctly describes the definition of independent increment proces...

Beginner

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Core Properties

4 questions

Question 2: Mean Function Additivity

Let {X(t); t ≥ 0} be an independent increment process with X(0) = 0. If E[X(2)] = 4 and E[X(5)] = 10...

Intermediate

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Question 3: Covariance Function Simplification

Let {X(t); t ≥ 0} be an independent increment process with X(0) = 0 and D[X(3)] = 9. Then Cov[X(3), ...

Intermediate

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Question 4: Mean Square Value Relationship

Let {X(t); t ≥ 0} be an independent increment process with X(0) = 0, E[X(4)] = 8, and D[X(4)] = 16. ...

Advanced

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Question 5: Markov Property Relationship

Which of the following statements about the relationship between independent increment processes and...

Advanced

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Random Walk Applications

3 questions

Question 6: Random Walk Mean Function

In a simple random walk {Sₙ} with p = 0.6 and q = 0.4, E[S₅] equals:...

Intermediate

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Question 7: Random Walk Variance

In a simple random walk {Sₙ} with p = q = 0.5, D[S₈] equals:...

Intermediate

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Question 8: Random Walk Probability

In a simple random walk {Sₙ} with p = q = 0.5, P{S₃ = 1} equals:...

Advanced

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Process Types

1 questions

Question 9: Process Classification

Which of the following processes is necessarily an independent increment process?...

Intermediate

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Advanced Properties

1 questions

Question 10: Normal Distribution Properties

Let {X(t); t ≥ 0} be an independent increment process with X(0) = 0, X(2) ~ N(4, 9), and X(5) - X(2)...

Advanced

Not attempted

Independent Increment Processes Practice

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