توضیح 1
Point mass: dpois gives exactly x events.
Loading
Loading
درس 12 از 18
Calculate Poisson point and tail probabilities while matching lambda to the requested exposure.
Core lesson
Calculate Poisson point and tail probabilities while matching lambda to the requested exposure.
توضیح 1
Point mass: dpois gives exactly x events.
توضیح 2
Cumulative mass: ppois gives at most x events.
توضیح 3
Rate scaling: Multiply lambda by the exposure ratio.
اصطلاحات
dpois gives exactly x events.
Exactly ten calls.
ppois gives at most x events.
At most ten calls.
Multiply lambda by the exposure ratio.
30-minute to 90-minute rate.
نمادگذاری و فرمولها
P(X=x)=exp(-lambda)lambda^x/x!
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Inspect the event-count PMF for a selected rate.
P(X = x)
0.1339
F(x) = P(X <= x)
0.2851
E(X)
5.9916
SD(X)
2.4379
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.0025 | Yes |
| 1 | 0.0149 | Yes |
| 2 | 0.0446 | Yes |
| 3 | 0.0892 | Yes |
| 4 | 0.1339 | Yes |
| 5 | 0.1606 | No |
| 6 | 0.1606 | No |
| 7 | 0.1377 | No |
| 8 | 0.1033 | No |
| 9 | 0.0688 | No |
| 10 | 0.0413 | No |
| 11 | 0.0225 | No |
| 12 | 0.0113 | No |
| 13 | 0.0052 | No |
| 14 | 0.0022 | No |
| 15 | 0.0009 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
فعالیت تعاملی
Scale lambda only after matching the exposure units.
P(X = x)
0.1339
F(x) = P(X <= x)
0.2851
E(X)
5.9916
SD(X)
2.4379
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.0025 | Yes |
| 1 | 0.0149 | Yes |
| 2 | 0.0446 | Yes |
| 3 | 0.0892 | Yes |
| 4 | 0.1339 | Yes |
| 5 | 0.1606 | No |
| 6 | 0.1606 | No |
| 7 | 0.1377 | No |
| 8 | 0.1033 | No |
| 9 | 0.0688 | No |
| 10 | 0.0413 | No |
| 11 | 0.0225 | No |
| 12 | 0.0113 | No |
| 13 | 0.0052 | No |
| 14 | 0.0022 | No |
| 15 | 0.0009 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
مثال حلشده
سناریو
A support desk plans for an hourly interval from a 15-minute rate.
A unit mismatch can be four times more consequential than rounding.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Model arrivals, scale rates to matching units, and compare observed mean and variance.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
State lambda with its exposure units every time it is used or scaled.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through Poisson Probabilities and Rate Scaling by asking about X, support, parameters, assumptions, probability notation, exact versus approximate status, and interpretation. Do not provide a quiz answer before submission or write my final capstone recommendation.
ارزیابی پایانی
منبع
Explore additional discrete-distribution explanations from properly licensed or publisher resources.
دریافتمنبع
Download an original worksheet, formula sheet, or capstone tool for this lesson.
دریافت