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Calculate PDF, CDF, survival probability, and interval probability for a continuous uniform distribution
Details
Calculate probabilities for a continuous uniform distribution over a finite range [a, b].
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Uniform Distribution Calculator is a statistical utility designed to compute the Probability Density Function (PDF), Cumulative Distribution Function (CDF), and interval probabilities for a continuous uniform distribution. By defining the minimum and maximum bounds of your dataset, you can instantly determine the likelihood of specific outcomes or ranges occurring within a perfectly flat probability model.
Background
A subway train arrives exactly every 15 minutes. A passenger arrives at the station at a random time.
Problem
Determine the probability that the passenger will wait 5 minutes or less.
How to use
Set the minimum to 0 and maximum to 15. Enter 5 as the target value.
Minimum: 0, Maximum: 15, Value: 5Outcome
The calculator returns a CDF of 0.3333, meaning there is a 33.33% chance the wait time will be 5 minutes or less.
Background
A machine cuts pipes to lengths uniformly distributed between 100 cm and 105 cm.
Problem
Find the probability that a randomly selected pipe falls within the acceptable tolerance range of 101 cm to 103 cm.
How to use
Input 100 as the minimum and 105 as the maximum. Set the Interval Lower to 101 and Interval Upper to 103.
It is a probability distribution where all values within a specified continuous range [a, b] are equally likely to occur, resulting in a flat, rectangular probability density.
The Probability Density Function (PDF) represents the constant probability density for any value within the defined minimum and maximum bounds. It is calculated as 1 divided by the difference between the maximum and minimum.
The Cumulative Distribution Function (CDF) calculates the probability that a random variable is less than or equal to your specified target value.
Yes, by entering values into the optional Interval Lower and Interval Upper fields, the tool will calculate the exact probability of an outcome falling within that specific range.
Minimum: 100, Maximum: 105, Interval Lower: 101, Interval Upper: 103Outcome
The tool calculates an interval probability of 0.4000, indicating a 40% chance the pipe meets the specific tolerance.
If the value is below the minimum, the CDF is 0. If it is above the maximum, the CDF is 1. The PDF outside the bounds is always 0.