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All 8 Flashcards — Poisson distribution
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Question
State the Poisson probability formula.
Answer
For X ~ Po(m): P(X = x) = e^(−m)·mˣ/x!, for x = 0, 1, 2, …
Question
What does the parameter m represent in Po(m)?
Answer
The mean (average) number of events in the fixed interval.
Question
For a Poisson distribution, how do the mean and variance compare?
Answer
They are EQUAL: mean = variance = m, so σ = √m.
Question
Which GDC function gives P(X = x) for a Poisson?
Answer
poissonpdf(m, x) — the probability of exactly x events.
Question
Which GDC function gives P(X ≤ x) for a Poisson?
Answer
poissoncdf(m, x) — the probability of at most x events.
Question
How do you find P(X ≥ k) for a Poisson on the GDC?
Answer
Use the complement: P(X ≥ k) = 1 − poissoncdf(m, k − 1).
Question
If X ~ Po(m₁) and Y ~ Po(m₂) are independent, what is X + Y?
Answer
Also Poisson: X + Y ~ Po(m₁ + m₂) — the means add.
Question
List conditions for a Poisson model to be suitable.
Answer
Events occur independently, at a constant average rate, singly (not in clumps), with no fixed upper limit on the count.
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Topic 4.17 hub
Poisson distribution (HL only)
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