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