توضیح 1
PMF: p(x)=P(X=x), the mass at one value.
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درس 3 از 18
Use PMF and CDF views to answer exact, cumulative, interval, and tail questions.
Core lesson
Use PMF and CDF views to answer exact, cumulative, interval, and tail questions.
توضیح 1
PMF: p(x)=P(X=x), the mass at one value.
توضیح 2
CDF: F(x)=P(X<=x), cumulative probability through x.
توضیح 3
Tail: Probability beyond a threshold.
اصطلاحات
p(x)=P(X=x), the mass at one value.
Exactly 55 requests.
F(x)=P(X<=x), cumulative probability through x.
At most 55 requests.
Probability beyond a threshold.
More than 55 requests.
نمادگذاری و فرمولها
p(x)=P(X=x); F(x)=P(X<=x)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Compare point mass with cumulative probability through a selected x.
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.
فعالیت تعاملی
Translate exactly, at most, fewer than, more than, and at least.
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 desk can handle 55 requests before overtime.
A one-integer boundary error changes the decision probability.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Build PMF and CDF tables and answer exact, cumulative, and tail queries.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
For integer X, fewer than x is P(X<=x-1), while at least x is 1-P(X<=x-1).
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through Probability Mass Functions and Cumulative Distribution Functions 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