# Exponential distribution Probabilities

Calculator of Exponential distribution : probabilities, density function (PDF) and cumulative density function (CDF).

## Exponential Distribution formulas

X : a random variable following a Exponential distribution of parameter `lambda > 0`.

### Probability Density Function (PDF)

`f(x) = lambda*exp(-lambda*x)` for `x >= 0`

### Cumulative distribution function (CDF)

`F(x) = \int_-oo^x f(t)\ dt`

`F(x) = 1-exp(-lambda*x)` for `x >= 0`

### Probabilities

Probability that X is greater than a :

`P(X > a) = 1 - F(a)`

Probability that X is less than b :

`P(X < b) = F(b)`

Probability that X lies between a and b :

`P(a < X < b) = F(b) - F(a)`

## See also

Inverse Exponential distribution

Exponential distribution Chart

Statistics Calculators