Uniform distribution Probabilities

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

M > m
(optional) b > a

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`


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