Statistics

Uniform Distribution Calculator

Find probabilities and stats for a continuous uniform distribution.

Calculated Output

P(X ≤ x) 0.7

Mean 5

Variance 8.333

Formula: P(X ≤ x) = (x − a)/(b − a)

Step-by-Step Breakdown

1. Values used:

2. Lower bound a = 0

3. Upper bound b = 10

4. Value x = 7

6. P(X ≤ x) = 0.7

7. Mean = 5

8. Variance = 8.333

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The math behind it

P(X ≤ x) = (x − a)/(b − a). Mean = (a+b)/2, variance = (b−a)²/12.

a 0, b 10, x 7 → P 0.7, mean 5.

Discrete vs continuous uniform?

Discrete assigns equal probability to each of n outcomes; this is the continuous version.