توضیح 1
Course X: Number of trials until first success, starting at one.
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درس 16 از 18
Model trials until the first success while translating the course convention to base R.
Advanced / Optional
Model trials until the first success while translating the course convention to base R.
توضیح 1
Course X: Number of trials until first success, starting at one.
توضیح 2
Base R value: Number of failures before success, starting at zero.
توضیح 3
Memoryless model: Future waiting does not depend on prior failures under constant p.
اصطلاحات
Number of trials until first success, starting at one.
Fourth contact converts.
Number of failures before success, starting at zero.
Three failures.
Future waiting does not depend on prior failures under constant p.
Stable independent contacts.
نمادگذاری و فرمولها
P(X=x)=(1-p)^(x-1)p, x=1,2,...
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Use trials until first success while displaying base R's offset.
P(X = x)
0.1024
F(x) = P(X <= x)
0.5904
E(X)
3.8318
SD(X)
2.8415
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 1 | 0.2 | Yes |
| 2 | 0.16 | Yes |
| 3 | 0.128 | Yes |
| 4 | 0.1024 | Yes |
| 5 | 0.0819 | No |
| 6 | 0.0655 | No |
| 7 | 0.0524 | No |
| 8 | 0.0419 | No |
| 9 | 0.0336 | No |
| 10 | 0.0268 | No |
| 11 | 0.0215 | No |
| 12 | 0.0172 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
R convention: course x=4 trials maps to dgeom(3, prob=p).
مثال حلشده
سناریو
A team counts contacts through the first conversion.
Customer heterogeneity can violate constant p and independence.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Use the course trials-until-success convention with base R functions.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Do not mix trials-until-success with failures-before-success; state which parameterization is used.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through The Geometric Distribution and Waiting Time 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