Explanation 1
Trial: One repeatable opportunity for the event.
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Lesson 7 of 18
Represent one binary trial with a clearly named success event and probability p.
Core lesson
Represent one binary trial with a clearly named success event and probability p.
Explanation 1
Trial: One repeatable opportunity for the event.
Explanation 2
Success: The event coded one, not necessarily a desirable result.
Explanation 3
Parameter p: The model probability of success.
Terminology
One repeatable opportunity for the event.
One completed service.
The event coded one, not necessarily a desirable result.
Service is late.
The model probability of success.
Late-service probability.
Notation and formulas
E(X)=p; Var(X)=p(1-p)
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
Define the binary success event before assigning p.
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.
Worked example
Scenario
Each completed service is classified late or on time.
A changing shift mix can make a single p unsuitable.
R connection
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Simulate Bernoulli trials and validate a binomial probability model.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Success is a mathematical label; define it explicitly and do not imply desirability.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
Coach me through Bernoulli Experiments 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%.
Resource
Explore additional discrete-distribution explanations from properly licensed or publisher resources.
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