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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

  1. 1PDF: f(x) = λe^(-λx)
  2. 2CDF: F(x) = 1 - e^(-λx)
  3. 3Mean = 1/λ, Variance = 1/λ²
  4. 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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