Counts of random events at a mean rate λ - calls per hour, flaws per metre - without the e^(−λ) formula.
In short: The Poisson distribution models the number of events occurring in a fixed interval when events happen independently at a constant average rate. The GDC's Poisson pdf gives P(X = k) and its cumulative function gives P(X ≤ k). Enter the mean and the value k, and find P(X ≥ k) as one minus a cumulative probability.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | 2nd → DISTR → poissonpdf(λ, r) for exactly r; poissoncdf(λ, r) for at most r. | Statistics → DIST (F5) → Poissn → Ppd (exactly) or Pcd (at most). | menu → Statistics → Distributions → Poisson Pdf / Poisson Cdf. |
Tip: Scale λ to the interval: 3 per hour over 20 minutes means λ = 1.
Tip: Scale λ to the interval: 3 per hour over 20 minutes means λ = 1.
Tip: Scale λ to the interval: 3 per hour over 20 minutes means λ = 1.
Here's a real IB-style question that uses exactly this technique.
Calls arrive at a helpdesk at a mean rate of 4 per hour, modelled by X ~ Po(4). Find (a) P(X = 6) and (b) P(X ≤ 6), each to 3 significant figures.
Counts of random events at a mean rate λ - calls per hour, flaws per metre - without the e^(−λ) formula. Random events happen independently at a known constant average rate (per hour, per metre, per page). A question asks for P(X = k) or P(X ≤ k) for a Poisson variable with mean λ.
1. Identify λ for the interval in the question (scale it if the interval changes). 2. 2nd → DISTR → poissonpdf(λ, r) for exactly r; poissoncdf(λ, r) for at most r. 3. ‘At least r’ = 1 − cdf(r−1). Independent Poissons add: λ_total = λ₁ + λ₂.
1. Identify λ for the interval in the question (scale it if the interval changes). 2. Statistics → DIST (F5) → Poissn → Ppd (exactly) or Pcd (at most). 3. ‘At least r’ = 1 − cdf(r−1). Independent Poissons add: λ_total = λ₁ + λ₂.
1. Identify λ for the interval in the question (scale it if the interval changes). 2. menu → Statistics → Distributions → Poisson Pdf / Poisson Cdf. 3. ‘At least r’ = 1 − cdf(r−1). Independent Poissons add: λ_total = λ₁ + λ₂.
Scale λ to the interval: 3 per hour over 20 minutes means λ = 1.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: poissonpdf(4, 6) and poissoncdf(4, 6); A1: P(X = 6) = 0.104; A1: P(X ≤ 6) = 0.889.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.