توضیح 1
Support: The distinct values X may take.
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درس 2 از 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.
توضیح 1
Support: The distinct values X may take.
توضیح 2
Probability mass: P(X=x) assigned to one support value.
توضیح 3
Valid distribution: Unique x values, mass in [0,1], and total one.
اصطلاحات
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.
نمادگذاری و فرمولها
p(x) >= 0 and sum_x p(x) = 1
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
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.
مثال حلشده
سناریو
A planner proposes five possible demand levels with probabilities.
Never normalize an invalid input silently.
ارتباط با R
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.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
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.
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