Let the r.v. **x** be uniformly distributed between **a** and **b**.
In this case,

the cdf is easily found to be

Now sample a random number from , set it equal to , and
solve for **x**:

which yields a sampled point **x** that is uniformly distributed on the interval
.

Consider the penetration of neutrons in a shield, where the pdf for the
distance **x** to collision is described by the exponential distribution,

A distance **x** to collision is then determined by first sampling a value for
the cdf from and solving for **x**.

One does not need to subtract the random number from unity, because and are both uniformly distributed on [0,1], and statistically the results will be identical.