Jinsi ya kukokotoa Exponential Dist
Exponential Dist ni nini?
Analyzes exponential distribution (waiting time) with mean 1/λ, used for modeling queues and failures.
Fomula
Mean = 1/λ, Variance = 1/λ²
Mwongozo wa Hatua kwa Hatua
- 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)
Mifano Iliyotatuliwa
Ingizo
λ=0.5, x=2
Matokeo
P=0.368
Makosa ya Kawaida ya Kuepuka
- ✕Using normal distribution for time data (exponential better)
- ✕Wrong λ parameter (rate, not 1/rate)
- ✕Not checking memoryless property applicability
Maswali yanayoulizwa mara kwa mara
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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