# Uniform distribution Probabilities

Calculator of Uniform distribution with m as minimum (lower bound) and M as maximum (upper bound).

## Uniform Distribution formulas

X : a random variable following a uniform distribution

m : lower bound or minimum value of X

M : upper bound or maximum value of X

### Probability Density Function (PDF)

`f(x) = 1/(M-m)` if `m<=x<=M`

`f(x) = 0` si `x < m` or `x > M`

### Cumulative distribution function (CDF)

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

By replacing f (above formula), we obtain,

`F(x) = 0` for `x < m`

`F(x) = (x-m)/(M-m)` for `m<=x<=M`

`F(x) = 1` for `x > M`

### 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 Uniform distribution

Statistics Calculators