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Analyzes exponential distribution (waiting time) with mean 1/λ, used for modeling queues and failures.
सूत्र
Mean = 1/λ, Variance = 1/λ²
चरण-दर-चरण मार्गदर्शिका
- 1PDF: f(x) = λe^(-λx)
- 2CDF: F(x) = 1 - e^(-λx)
- 3Mean = 1/λ, Variance = 1/λ²
- 4Memoryless property: P(X > s+t | X > s) = P(X > t)
हल किए गए उदाहरण
इनपुट
λ=0.5, x=2
परिणाम
P=0.368
सामान्य गलतियां जिनसे बचना है
- ✕Using normal distribution for time data (exponential better)
- ✕Wrong λ parameter (rate, not 1/rate)
- ✕Not checking memoryless property applicability
अक्सर पूछे जाने वाले प्रश्न
What's practical use?
Customer arrivals (Poisson), equipment failures, radioactive decay, service times.
What's memoryless property?
Past waiting time doesn't affect future; no "aging" effect.
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