Master Poisson processes theory with 10 comprehensive questions covering definitions, properties, distributions, and applications to counting processes.
10
Total Questions
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Questions Attempted
Core Properties
3 questions
Question 1: Poisson Process Increment Mean
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 3. Then E[N(4) - N(1)] equals:...
Beginner
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Question 2: Poisson Process Covariance
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 2. Then Cov[N(2), N(5)] equals:...
Intermediate
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Question 4: Conditional Distribution
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 1. Given N(5) = 3, then P{N(2) = 1 | N(5) ...
Advanced
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Key Distributions
4 questions
Question 3: Time Interval Distribution
The time interval T₁ (time to first event) in a Poisson process {N(t)} follows which distribution?...
Intermediate
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Question 6: Event Occurrence Time Mean
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 2. The mean of the 4th event occurrence ti...
Intermediate
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Question 8: Conditional Uniform Distribution
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 1. Given exactly one event in (0, 5], the ...
Advanced
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Question 9: Time Interval Distribution Function
Let {N(t); t ≥ 0} be a Poisson process with intensity λ = 3. The distribution function F_{T₂}(2) of ...
Advanced
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Advanced Properties
2 questions
Question 5: Non-Homogeneous Poisson Process
For a non-homogeneous Poisson process with intensity function λ(t) = t, the increment N(3) - N(1) fo...
Advanced
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Question 10: Non-Homogeneous Process Mean
For a non-homogeneous Poisson process with intensity function λ(t) = e^t, E[N(2) - N(0)] equals:...
Advanced
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Synthesis & Decomposition
1 questions
Question 7: Poisson Process Synthesis
Let {N₁(t)} (intensity λ₁ = 2) and {N₂(t)} (intensity λ₂ = 3) be independent Poisson processes. Then...
Intermediate
Not attempted
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