توضیح 1
Population N: Total finite items.
Loading
Loading
درس 14 از 18
Calculate exact success counts when sampling without replacement from a finite population.
Core lesson
Calculate exact success counts when sampling without replacement from a finite population.
توضیح 1
Population N: Total finite items.
توضیح 2
Successes K: Target items in the population.
توضیح 3
Sample n: Items drawn without replacement.
اصطلاحات
Total finite items.
Eighty components.
Target items in the population.
Twelve defectives.
Items drawn without replacement.
Ten inspected items.
نمادگذاری و فرمولها
P(X=x)=C(K,x)C(N-K,n-x)/C(N,n)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Model a finite population sampled without replacement.
P(X = x)
0.0329
F(x) = P(X <= x)
0.9945
E(X)
1.5
SD(X)
1.0629
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.1766 | Yes |
| 1 | 0.3592 | Yes |
| 2 | 0.2963 | Yes |
| 3 | 0.1295 | Yes |
| 4 | 0.0329 | Yes |
| 5 | 0.005 | No |
| 6 | 0.0005 | No |
| 7 | 0 | No |
| 8 | 0 | No |
| 9 | 0 | No |
| 10 | 0 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
مثال حلشده
سناریو
Ten items are drawn without replacement from a known lot.
Draws are dependent because the lot composition changes.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Map finite-population parameters and calculate probabilities without replacement.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Map R parameters as dhyper(x,m=K,n=N-K,k=sample_size); do not confuse both meanings of n.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through The Hypergeometric 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