توضیح 1
Exposure: A fixed time, area, volume, or other opportunity.
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درس 11 از 18
Evaluate whether a stable-rate event-count model is reasonable for a fixed exposure.
Core lesson
Evaluate whether a stable-rate event-count model is reasonable for a fixed exposure.
توضیح 1
Exposure: A fixed time, area, volume, or other opportunity.
توضیح 2
Rate lambda: Expected event count for that exposure.
توضیح 3
Process assumption: Roughly independent occurrences at a stable rate.
اصطلاحات
A fixed time, area, volume, or other opportunity.
Thirty minutes.
Expected event count for that exposure.
Seven calls per 30 minutes.
Roughly independent occurrences at a stable rate.
No campaign surge.
نمادگذاری و فرمولها
X ~ Poisson(lambda)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Assess exposure, rate stability, independence, and clustering.
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 desk counts calls in equal half-hour intervals.
Mixtures and clustering can create overdispersion.
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
A count response alone is insufficient; inspect exposure, rate stability, dependence, and excess variability.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through Poisson Processes and Event Counts 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