 Let formula_6 be a real-valued, continuous random variable and let formula_151.If formula_153, then formula_154, so

If formula_156, then

so

Suppose formula_6 is a random variable with a cumulative distribution

where formula_161 is a fixed parameter.Consider the random variable formula_162 Then,

The last expression can be calculated in terms of the cumulative distribution of formula_164 so

which is the cumulative distribution function (CDF) of an exponential distribution.