How this calculation works
Find the probability of a Rayleigh magnitude falling between two nonnegative bounds.
THE FORMULA
P(a≤X≤b)=exp(−a²/(2σ²))−exp(−b²/(2σ²))A worked example
For scale 2 and bounds 0 and 2, the probability is 1−exp(−1/2).
Good to know
The distribution’s scale must be positive.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Find the probability of a Rayleigh magnitude falling between two nonnegative bounds.
The primary result is labeled “Interval probability”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The distribution’s scale must be positive.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
For scale 2 and bounds 0 and 2, the probability is 1−exp(−1/2).
Which rule does this calculator apply?
P(a≤X≤b)=exp(−a²/(2σ²))−exp(−b²/(2σ²))