Continuous Uniform Probability Calculator

Calculate the probability for a continuous uniform distribution within a given range. Visualize the distribution and understand the probability area.

Lower Bound (a):

Upper Bound (b):

Range Lower Bound (c):

Range Upper Bound (d):

Probability: P(c ≤ X ≤ d)

Probability calculated using the formula: $$P(c \leq X \leq d) = \frac{d - c}{b - a}$$

Visualization of Uniform Distribution

Understanding Continuous Uniform Probability

The Continuous Uniform Distribution, also known as a rectangular distribution, is a probability distribution where every value over a given interval has an equal chance of occurring. It is defined by a lower bound (a) and an upper bound (b). The probability of a random variable X falling within any interval [c, d] that is within [a, b] is proportional to the length of the interval (d-c).

Probability Density Function (PDF): Constant between a and b, given by $$f(x) = \frac{1}{b-a}$$ for a ≤ x ≤ b, and 0 otherwise.
Cumulative Distribution Function (CDF): Increases linearly from 0 to 1 between a and b.
Use Cases: Modeling situations where all outcomes in a range are equally likely, such as random number generation or scenarios with constant rates.
Formula for Probability: $$P(c \leq X \leq d) = \frac{d - c}{b - a}$$, where [c, d] is a subinterval within [a, b].

Learn more about uniform distribution on resources like Wikipedia.