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ماژول 7: توزیعهای احتمال پیوسته | STATLAB Academy
ماژول 7
توزیعهای احتمال پیوسته خانه / ماژولها / ماژول 7 کاربرد مساحت احتمال، مدلهای کراندار، نرمال و نرمال معکوس، تقریب با تصحیح پیوستگی، قابلیت اطمینان نمایی و سناریوهای مثلثی در تصمیمهای کسبوکار.
شروع ماژول اهداف یادگیری تا پایان این ماژول، دانشجو میتواند: 1 Classify a business random variable as discrete or continuous at a stated measurement scale. 2 Calculate and interpret interval probability from a valid PDF or CDF. 3 Interpret a continuous variables, pdfs, cdfs, and probability as area result in business context with consistent units. 4 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation. 5 Calculate uniform probabilities, mean, variance, and standard deviation from endpoints. 6
Assess whether equal plausibility across a bounded interval is defensible.
7 Interpret a continuous uniform distribution result in business context with consistent units.
8 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
9 Explain how mean and standard deviation control a normal model.
10 Use process knowledge and diagnostics to assess approximate normality.
11 Interpret a normal distribution: shape, parameters, and fit result in business context with consistent units.
12 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
13 Standardize a normal value and interpret its signed distance from the mean.
14 Calculate and communicate left-tail, right-tail, and interval normal probabilities.
15 Interpret a standard normal and normal probabilities result in business context with consistent units.
16 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
17 Find a normal quantile from a left-tail, right-tail, or central probability.
18 Translate a percentile threshold into a feasible business rule.
19 Interpret a inverse normal: percentiles, thresholds, and service levels result in business context with consistent units.
20 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
21 Decide whether a normal approximation is reasonable for a binomial or Poisson count.
22 Apply continuity correction and quantify approximation error against an exact result.
23 Interpret a normal approximations to binomial and poisson models result in business context with consistent units.
24 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
25 Calculate exponential left-tail, right-tail, and interval probabilities.
26 Evaluate the constant-rate and memoryless assumptions in an operations setting.
27 Interpret a exponential distribution and waiting-time risk result in business context with consistent units.
28 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
29 Solve inverse exponential thresholds and connect rate to MTBE or MTBF.
30 Design a warranty or service threshold with an explicit reliability assumption.
31 Interpret a inverse exponential, mtbe/mtbf, reliability, and warranty result in business context with consistent units.
32 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
33 Calculate and simulate a triangular scenario from valid parameters.
34 Explain when triangular assumptions are more transparent than uniform or normal assumptions.
35 Interpret a optional: triangular distribution for what-if analysis result in business context with consistent units.
36 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
37 Select a candidate continuous model and justify it from process evidence.
38 Diagnose model risk using support, shape, stability, and sensitivity checks.
39 Interpret a continuous model selection and assumption audit result in business context with consistent units.
40 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
41 Build an auditable multi-model analysis with exact-versus-approximate checks.
42 Defend an operational recommendation using probabilities, thresholds, limitations, and reproducible R.
43 Interpret a capstone: northstar operations risk lab result in business context with consistent units.
44 Use and explain the relevant base R distribution functions without confusing density, probability, quantiles, or simulation.
درسها 1
متغیرهای پیوسته، PDF، CDF و احتمال بهعنوان مساحت Move from count probabilities to measurement models and connect density, cumulative probability, and interval area.
باز کردن 2
توزیع یکنواخت پیوسته Use bounded equal-density models for transparent interval and what-if calculations.
باز کردن 3
توزیع نرمال: شکل، پارامترها و برازش Read the normal curve as a family indexed by mean and standard deviation, then challenge its suitability.
باز کردن 4
نرمال استاندارد و احتمالهای نرمال Translate business thresholds into z scores and compute left, right, and middle areas reliably.
باز کردن 5
نرمال معکوس: صدکها، آستانهها و سطح خدمت Reverse the normal CDF to turn coverage targets into operational thresholds.
باز کردن 6
تقریب نرمال برای مدلهای دوجملهای و پواسون Use rule checks and continuity correction, then compare approximate and exact probabilities.
باز کردن 7
توزیع نمایی و ریسک زمان انتظار Model waiting time between stable independent events and calculate operational tail risk.
باز کردن 8
نمایی معکوس، MTBE/MTBF، قابلیت اطمینان و ضمانت Turn target service and failure probabilities into time thresholds while challenging constant hazard.
باز کردن 9
اختیاری: توزیع مثلثی برای تحلیل چه-میشود-اگر Build a transparent bounded scenario from minimum, most-likely, and maximum values.
باز کردن 10
انتخاب مدل پیوسته و ممیزی فرضها Choose among uniform, normal, exponential, and triangular models using mechanism, support, shape, and decision risk.
باز کردن 11
پروژه نهایی: آزمایشگاه ریسک عملیاتی نورثاستار Integrate service, arrival, quality, lifetime, and project-risk models into an original executive recommendation.
باز کردن کتابخانه مدلسازی پیوسته
آزمایشگاههای R، دادههای مصنوعی، کاربرگها و ابزارهای پروژه نهایی همه مثالها، مقادیر، اسکریپتها، پرسشها و مجموعهدادهها تولید اصیل آکادمی STATLAB هستند. ماژول ۶ پیشنیاز پیشنهادی احتمال است. اصطلاحات فارسی برای بازبینی علمی انسانی جداگانه ارائه میشود؛ فرمولها، R و نام ستونها چپبهراست میمانند.
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