توضیح 1
Trial: One repeatable opportunity for the event.
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درس 7 از 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.
توضیح 1
Trial: One repeatable opportunity for the event.
توضیح 2
Success: The event coded one, not necessarily a desirable result.
توضیح 3
Parameter p: The model probability of success.
اصطلاحات
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.
نمادگذاری و فرمولها
E(X)=p; Var(X)=p(1-p)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
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.
مثال حلشده
سناریو
Each completed service is classified late or on time.
A changing shift mix can make a single p unsuitable.
ارتباط با R
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.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
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.
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