توضیح 1
Equal mass: Every supported integer has probability 1/k.
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درس 6 از 18
Model equally likely consecutive integers and compare theoretical with simulated frequencies.
Core lesson
Model equally likely consecutive integers and compare theoretical with simulated frequencies.
توضیح 1
Equal mass: Every supported integer has probability 1/k.
توضیح 2
Consecutive support: Integers a through b.
توضیح 3
Simulation: Repeated random draws from the model.
اصطلاحات
Every supported integer has probability 1/k.
Ten invoice numbers.
Integers a through b.
101, ..., 110.
Repeated random draws from the model.
A reproducible audit sample.
نمادگذاری و فرمولها
E(X)=(a+b)/2; Var(X)=((b-a+1)^2-1)/12
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Compare equal theoretical mass with a deterministic simulated pattern.
P(X = x)
0.1
F(x) = P(X <= x)
0.4
E(X)
5.5
SD(X)
2.8723
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 1 | 0.1 | Yes |
| 2 | 0.1 | Yes |
| 3 | 0.1 | Yes |
| 4 | 0.1 | Yes |
| 5 | 0.1 | No |
| 6 | 0.1 | No |
| 7 | 0.1 | No |
| 8 | 0.1 | No |
| 9 | 0.1 | No |
| 10 | 0.1 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
مثال حلشده
سناریو
A validated randomizer selects one of ten indexed invoices.
Administrative selection rules can destroy uniformity.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Compare simulated and theoretical results for equally likely integers.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Do not call a process uniform merely because its possible integers are consecutive.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through The Discrete Uniform Distribution 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