Uniform Distribution Calculator
Calculate PDF, CDF, mean and variance for the continuous uniform distribution on [a, b].
Inputs
PDF f(x)
0.10000000
P(X ≤ x)
0.30000000
Mean
5.0000
Variance
8.333333
Step by step
Values used
Lower Bound (a) = 0; Upper Bound (b) = 10; x value = 3
PDF
f(x) = 1/(b−a) for a ≤ x ≤ b, 0 otherwise
CDF
F(x) = (x−a)/(b−a) for a ≤ x ≤ b
PDF f(x)
= 0.10000000
P(X ≤ x)
= 0.30000000
Mean
= 5.0000
Variance
= 8.333333
How it works
The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. It is the simplest continuous distribution and serves as a model for 'equally likely' outcomes over a range.
Formulas
f(x) = 1/(b−a) for a ≤ x ≤ b, 0 otherwise
- a
- Lower bound
- b
- Upper bound
CDF
F(x) = (x−a)/(b−a) for a ≤ x ≤ b
- x
- Point of evaluation
Frequently Asked Questions
What is the probability of an exact value in a continuous uniform distribution?
Zero. For any continuous distribution, P(X = exact value) = 0. Probability only applies to intervals.
What real-world situations follow a uniform distribution?
Random number generators, arrival times within a known window, and rounding errors are often modeled as uniform.
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