Exponential Distribution Calculator

Find probabilities for an exponential distribution.

P(X ≤ x) 0.7769

Mean 2

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

Step-by-step with your numbers:

1. Values used:

2. Rate (λ) = 0.5

3. Value x = 3

5. P(X ≤ x) = 0.7769

6. Mean = 2

Did we solve your problem today?

The exponential distribution models waiting times between random events.

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.