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Continuous Uniform Probability Calculator
Easily calculate continuous uniform probability online. Determine the probability of a random variable falling within a specified range in a uniform distribution. Visualize the distribution and copy results.
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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.