continuous random variable

Formally, a continuous random variable is a random variable whose cumulative distribution function is continuous everywhere. Continuous random variables almost never take an exact prescribed value \[x\] (i.e. \[\forall x\in \mathbb{R}:P(X=x)=0\]).

A classic example for be the time it takes to complete an exam which has a time limit of 90 minutes. The possible times for a student completing the exam is \[x\in \left[ 0,90 \right]\], and since real numbers are infinitely dense, the probability of a student completing the exam at a particular time will become zero. Only the probability of the intervals (say from 75 to 80 minutes) in which they might finish can be measured.