Exponential Distribution Calculator
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Exponential Distribution Formulas
PDF: f(x) = λe^(-λx) for x ≥ 0
CDF: F(x) = 1 - e^(-λx) for x ≥ 0
Mean: μ = 1/λ
Variance: σ² = 1/λ²
Exponential distribution has the memoryless property: P(X > t+s | X > t) = P(X > s)!
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Exponential distribution is continuous and defined only for x ≥ 0.
What is Exponential Distribution?
Exponential distribution models the time between events in a Poisson point process, and is famous for its memoryless property.
Continuous Distribution
For positive real numbers
Memoryless Property
No aging effect
Single Parameter
Rate parameter λ
Mean = Std Dev
μ = σ = 1/λ
💡 Example: λ=0.5, x=2 → f(x)=0.184, F(x)=0.632, μ=2, σ=2
Applications
Queuing Theory
Reliability
Survival Analysis
Network Traffic
Physics
Frequently Asked Questions
What is exponential distribution?▼
Exponential distribution models time between events in a Poisson process, with memoryless property.
What is PDF of exponential distribution?▼
f(x) = λe^(-λx) for x ≥ 0.
What is CDF of exponential distribution?▼
F(x) = 1 - e^(-λx) for x ≥ 0.
What is mean and variance?▼
Mean μ = 1/λ, Variance σ² = 1/λ², Standard deviation σ = 1/λ.
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