Continuous uniform distribution
Example 2. Using the continuous uniform distribution function (conditional)

For a random variable X ∼ U (0, 23), {\displaystyle X\sim U(0,23),} find P (X > 12 | X > 8): {\displaystyle P(X>12\ |\ X>8):}

The example above is a conditional probability case for the continuous uniform distribution: given that X > 8 {\displaystyle X>8} is true, what is the probability that X > 12 ? {\displaystyle X>12?} Conditional probability changes the sample space, so a new interval length b − a ′ {\displaystyle b-a'} has to be calculated, where b = 23 {\displaystyle b=23} and a ′ = 8. {\displaystyle a'=8.} The graphical representation would still follow Example 1, where the area under the curve within the specified bounds displays the probability; the base of the rectangle would be 11, {\displaystyle 11,} and the height would be 1 15. {\displaystyle {\tfrac {1}{15}}.}
startend:end_checker, punctuation:no_comma