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Stochastic Process Fundamentals Practice

Master the fundamentals of stochastic processes with 15 comprehensive questions covering definitions, classification, numerical characteristics, Gaussian processes, and advanced topics.

15
Total Questions
0
Correct Answers
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Questions Attempted
Basic Concepts
3 questions
Question 1: Stochastic Process Definition
A stochastic process {X(t); t ∈ T} is best defined as:...
Beginner
Not attempted
Question 2: State Space Classification
A random walk where Sₙ = X₁ + X₂ + ... + Xₙ with Xᵢ ∈ {-1, +1} has which type of state space?...
Beginner
Not attempted
Question 3: Sample Function Interpretation
For a stochastic process {X(t); t ∈ T}, a sample function represents:...
Intermediate
Not attempted
Classification
1 questions
Question 4: Process Classification by Time
Which of the following is an example of a continuous-time discrete-state process?...
Beginner
Not attempted
Distributions
1 questions
Question 5: Finite-Dimensional Distributions
The finite-dimensional distribution family of a stochastic process completely determines:...
Intermediate
Not attempted
Numerical Characteristics
3 questions
Question 6: Mean Function Properties
For the stochastic process X(t) = At + B where A and B are independent random variables, the mean fu...
Beginner
Not attempted
Question 7: Second-Order Moment Process
A stochastic process {X(t)} is called a second-order moment process if:...
Intermediate
Not attempted
Question 8: Autocovariance Function
The relationship between autocovariance Cₓ(s,t) and autocorrelation Rₓ(s,t) is:...
Intermediate
Not attempted
Special Processes
2 questions
Question 9: Gaussian Process Definition
A stochastic process {X(t)} is Gaussian (normal) if and only if:...
Advanced
Not attempted
Question 10: Gaussian Process Properties
For a Gaussian process, which statement is TRUE?...
Advanced
Not attempted
Multi-Dimensional Processes
2 questions
Question 11: Two-Dimensional Processes
For two stochastic processes {X(t)} and {Y(t)}, the cross-covariance function is:...
Intermediate
Not attempted
Question 12: Process Independence
Two stochastic processes {X(t)} and {Y(t)} are independent if:...
Intermediate
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Advanced Topics
3 questions
Question 13: Stationary Process Basics
A strictly stationary process has the property that:...
Advanced
Not attempted
Question 14: Process Sum Properties
If {X(t)} and {Y(t)} are uncorrelated processes, then for Z(t) = X(t) + Y(t), the autocovariance is:...
Advanced
Not attempted
Question 15: Ergodic Process Concept
Ergodicity in stochastic processes relates:...
Advanced
Not attempted

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