Explanation 1
Support: The distinct values X may take.
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Lesson 2 of 18
Construct a custom PMF and verify unique support, nonnegative mass, and total probability one.
Core lesson
Construct a custom PMF and verify unique support, nonnegative mass, and total probability one.
Explanation 1
Support: The distinct values X may take.
Explanation 2
Probability mass: P(X=x) assigned to one support value.
Explanation 3
Valid distribution: Unique x values, mass in [0,1], and total one.
Terminology
The distinct values X may take.
40, 55, or 70 units.
P(X=x) assigned to one support value.
P(X=55)=0.45.
Unique x values, mass in [0,1], and total one.
A checked demand PMF.
Notation and formulas
p(x) >= 0 and sum_x p(x) = 1
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
Check unique values, probability bounds, and total probability.
P(X = x)
0.2
F(x) = P(X <= x)
0.9
E(X)
3
SD(X)
1.0954
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 1 | 0.1 | Yes |
| 2 | 0.2 | Yes |
| 3 | 0.4 | Yes |
| 4 | 0.2 | Yes |
| 5 | 0.1 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
Worked example
Scenario
A planner proposes five possible demand levels with probabilities.
Never normalize an invalid input silently.
R connection
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Validate a custom PMF without silently repairing it.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Normalization may be demonstrated only when clearly labelled; it must not conceal a data or modelling error.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
Coach me through Building and Validating a Discrete Probability 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
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