Uniform Distribution Calculator
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Uniform Distribution Formulas
PDF: f(x) = 1/(b-a) for a ≤ x ≤ b, else 0
CDF: F(x) = (x-a)/(b-a) for a ≤ x ≤ b
Mean: μ = (a+b)/2
Variance: σ² = (b-a)²/12
P(c ≤ X ≤ d) = (min(d,b) - max(c,a))/(b-a)
All intervals of equal length within [a,b] are equally probable!
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Ensure a < b for valid uniform distribution parameters.
What is Uniform Distribution?
Uniform distribution is a continuous probability distribution where all intervals of equal length on the distribution's support are equally probable.
Constant PDF
Equal probability density
Continuous
For real numbers
Interval [a,b]
Support defined by a and b
💡 Example: a=0, b=10, x=3 → f(x)=0.1, F(x)=0.3, μ=5, σ²≈8.333
Applications
Simulation
Random Number Generation
Statistics
Engineering
Education
Frequently Asked Questions
What is uniform distribution?▼
Uniform distribution has constant probability density over an interval [a,b].
What is PDF of uniform distribution?▼
f(x) = 1/(b-a) for a ≤ x ≤ b, else 0.
What is CDF of uniform distribution?▼
F(x) = (x-a)/(b-a) for a ≤ x ≤ b.
What is mean and variance?▼
Mean μ = (a+b)/2, Variance σ² = (b-a)²/12.
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