Explanation 1
Equal mass: Every supported integer has probability 1/k.
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Lesson 6 of 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.
Explanation 1
Equal mass: Every supported integer has probability 1/k.
Explanation 2
Consecutive support: Integers a through b.
Explanation 3
Simulation: Repeated random draws from the model.
Terminology
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.
Notation and formulas
E(X)=(a+b)/2; Var(X)=((b-a+1)^2-1)/12
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
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.
Worked example
Scenario
A validated randomizer selects one of ten indexed invoices.
Administrative selection rules can destroy uniformity.
R connection
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.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
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.
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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