Explanation 1
Course X: Number of trials until first success, starting at one.
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Lesson 16 of 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.
Explanation 1
Course X: Number of trials until first success, starting at one.
Explanation 2
Base R value: Number of failures before success, starting at zero.
Explanation 3
Memoryless model: Future waiting does not depend on prior failures under constant p.
Terminology
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.
Notation and formulas
P(X=x)=(1-p)^(x-1)p, x=1,2,...
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
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).
Worked example
Scenario
A team counts contacts through the first conversion.
Customer heterogeneity can violate constant p and independence.
R connection
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.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
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.
Exit check
Use conceptual hints before submitting. Full formulas, calculations, and interpretation appear afterward.
Checkpoint
Question 1 of 2. Answered 0/2. Passing score: 70%.
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