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A note on the exponential distribution

The exponential distribution is an example of a continuous distribution. A random variable X is said to follow the exponential distribution with parameter λ if its distribution function F is given by: F (x) = 1 − e−λ x for x > 0. Recall that the distribution function F (x) = P (X ≤ x) by definition and is an increasing function of x. Since F (0) = 0, it follows that X is bigger than 0 with probability 1.