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