It seems like you're asking about the distribution of a random variable that follows an exponential distribution with a cumulative distribution function (c.d.f). The exponential distribution is commonly defined by its probability density function (p.d.f), not the cumulative distribution function (c.d.f). The p.d.f. of an exponential random variable with parameter λ is given by:
f(x) = λ * e^(-λx) for x >= 0, and f(x) = 0 for x < 0.
To find the distribution of the random variable, you need to specify the parameter λ. Once you have the p.d.f., you can use it to calculate various properties, such as mean, variance, and percentiles, which fully describe the distribution of the random variable.
Hope this helps you