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Ako vypočítať Exponential Dist

Čo je Exponential Dist?

Analyzes exponential distribution (waiting time) with mean 1/λ, used for modeling queues and failures.

Vzorec

Mean = 1/λ, Variance = 1/λ²

Sprievodca krok za krokom

  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)

Worked Examples

Vstup
λ=0.5, x=2
Výsledok
P=0.368

Common Mistakes to Avoid

  • Using normal distribution for time data (exponential better)
  • Wrong λ parameter (rate, not 1/rate)
  • Not checking memoryless property applicability

Frequently Asked Questions

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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