Continuous random variable

Exponential distribution

An exponentially distributed random variable is common in situations of exponential decay, usually representing the amount of time taken for something to happen, e.g. the decay of a uranium nucleus (see Poisson process). It has positive support and is described by the following probability density function and Cumulative distribution function

may be thought of as the frequency of the event: the higher , the shorter the time before the event occurs. In fact, the expected period is exactly what one might assume by this analogy.

Properties

Let

  1. Expectation:
  2. Variance:
  3. Moment-generating function: for
  4. Moments:

Additionally


#state/tidy | #SemBr