poissonpdf & poissoncdf Calculator
Evaluate the TI-84 Poisson functions online. poissonpdf(λ, x) gives the probability of exactly x events when λ occur on average; poissoncdf(λ, x) gives the probability of at most x. The "at least", "fewer than", and "more than" versions are computed for you.
Part of the TI-84 statistics functions guide, which shows when to use poissonpdf and poissoncdf and every other DISTR-menu function.
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poissonpdf vs. poissoncdf
Both functions model counts of independent events that happen at a steady average rate λ over a fixed interval — calls per hour, typos per page, arrivals per minute.
poissonpdf(λ, x) = e^(−λ) · λˣ / x! = P(X = x)
poissoncdf(λ, x) = Σ poissonpdf(λ, k) for k = 0…x = P(X ≤ x)
Note the argument order: on the TI-84 the mean comes first, unlike binompdf where n and p come first. Swapping them is a common source of wrong answers.
Translating Word Problems
| Phrase | TI-84 entry |
|---|---|
| exactly 3 | poissonpdf(λ, 3) |
| at most 3 | poissoncdf(λ, 3) |
| fewer than 3 | poissoncdf(λ, 2) |
| at least 3 | 1 − poissoncdf(λ, 2) |
| more than 3 | 1 − poissoncdf(λ, 3) |
Worked Example: Calls to a Help Desk
A help desk receives an average of 2.5 calls per minute. What is the probability of exactly 3 calls in a minute, and of 4 or more?
- poissonpdf(2.5, 3) = e^(−2.5) × 2.5³ / 3! = 0.082085 × 15.625 / 6 = 0.213763.
- poissoncdf(2.5, 3) = P(0) + P(1) + P(2) + P(3) = 0.757576.
- At least 4 = 1 − poissoncdf(2.5, 3) = 0.242424.
About one minute in four is busy enough for 4+ calls. If the interval changes, scale λ: for a 2-minute window use λ = 5. For the distribution's mean, variance, and approximations, see the Poisson distribution calculator.
Where to Find poissonpdf on a TI-84
- Press 2nd then VARS (DISTR).
- Scroll to C:poissonpdf( or D:poissoncdf(.
- Enter μ (λ) and the x value, then select Paste and press ENTER.
In Excel use =POISSON.DIST(x, λ, FALSE) for poissonpdf and =POISSON.DIST(x, λ, TRUE) for poissoncdf.
Frequently Asked Questions
When do I use poissonpdf instead of binompdf?
Use Poisson when you know an average rate of events over an interval but there is no fixed number of trials — for example 2.5 calls per minute. Use binomial when there are n separate trials with the same success probability p.
How do I calculate 'at least' with poissoncdf?
P(X ≥ x) = 1 − poissoncdf(λ, x − 1). For at least 4 events with λ = 2.5, that is 1 − poissoncdf(2.5, 3) = 0.242424.
Can λ be a decimal?
Yes. λ is an average, so values like 2.5 or 0.3 are normal. Only x, the count of events, must be a whole number.
How do I change λ for a different time period?
Scale it proportionally. If a road averages 12 accidents per year, λ is 1 per month and 3 per quarter. The Poisson model assumes the rate is constant across the period.
What conditions does the Poisson distribution need?
Events occur one at a time, independently of each other, at a constant average rate. Clustering (such as rush-hour spikes) or a rate that changes during the interval breaks the model.
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