Statistics

Exponential Distribution Calculator

Find probabilities for an exponential distribution.

Calculated Output

P(X ≤ x) 0.7769

Mean 2

Formula: P(X ≤ x) = 1 − e^(−λx); mean = 1/λ

Step-by-Step Breakdown

1. Values used:

2. Rate (λ) = 0.5

3. Value x = 3

5. P(X ≤ x) = 0.7769

6. Mean = 2

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The math behind it

P(X ≤ x) = 1 − e^(−λx). The mean (average wait) is 1/λ.

λ 0.5, x 3 → P ≈ 0.777, mean 2.

What's the memoryless property?

The chance of waiting more doesn't depend on how long you've already waited.