توضیح 1
Exact model: The original fixed-trial binomial probability.
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درس 13 از 18
Compare exact binomial probabilities with a labelled Poisson approximation using lambda=np.
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Compare exact binomial probabilities with a labelled Poisson approximation using lambda=np.
توضیح 1
Exact model: The original fixed-trial binomial probability.
توضیح 2
Approximation: A Poisson value used when events are rare and n is large.
توضیح 3
Error: Difference between exact and approximate values.
اصطلاحات
The original fixed-trial binomial probability.
dbinom result.
A Poisson value used when events are rare and n is large.
dpois with lambda=np.
Difference between exact and approximate values.
Absolute or relative error.
نمادگذاری و فرمولها
Binomial(n,p) approximately Poisson(lambda=np)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Compare an exact binomial PMF with a labelled approximation.
P(X = x)
0.2182
F(x) = P(X <= x)
0.6296
E(X)
4
SD(X)
1.7889
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.0115 | Yes |
| 1 | 0.0576 | Yes |
| 2 | 0.1369 | Yes |
| 3 | 0.2054 | Yes |
| 4 | 0.2182 | Yes |
| 5 | 0.1746 | No |
| 6 | 0.1091 | No |
| 7 | 0.0545 | No |
| 8 | 0.0222 | No |
| 9 | 0.0074 | No |
| 10 | 0.002 | No |
| 11 | 0.0005 | No |
| 12 | 0.0001 | No |
| 13 | 0 | No |
| 14 | 0 | No |
| 15 | 0 | No |
| 16 | 0 | No |
| 17 | 0 | No |
| 18 | 0 | No |
| 19 | 0 | No |
| 20 | 0 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
Approximation safeguard: Treat the comparison model as approximate and inspect its error against the exact model.
مثال حلشده
سناریو
A large set of tickets has a small stable escalation probability.
Approximation quality varies by parameters and query.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Compare exact binomial and approximate Poisson probabilities.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Never present the Poisson approximation as exact; compare with the exact binomial whenever feasible.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through Poisson Approximation to the Binomial 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